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Deep Learning

Deep Learning allows computational models composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection, and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large datasets by using the back-propagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about dramatic improvements in processing images, video, speech and audio, while recurrent nets have shone on sequential data such as text and speech. Representation learning is a set of methods that allows a machine to be fed with raw data and to automatically discover the representations needed for detection or classification. Deep learning methods are representation learning methods with multiple levels of representation, obtained by composing simple but non-linear modules that each transform the representation at one level (starting with the raw input) into a representation at a higher, slightly more abstract level. This tutorial will introduce the fundamentals of deep learning, discuss applications, and close with challenges ahead.

Monday December 7, 2015 09:30 - 11:30

Level 2 room 210 AB

Level 2 room 210 AB

Large-Scale Distributed Systems for Training Neural Networks

Over the past few years, we have built large-scale computer systems for training neural networks, and then applied these systems to a wide variety of problems that have traditionally been very difficult for computers. We have made significant improvements in the state-of-the-art in many of these areas, and our software systems and algorithms have been used by dozens of different groups at Google to train state-of-the-art models for speech recognition, image recognition, various visual detection tasks, language modeling, language translation, and many other tasks. In this talk,we'll highlight some of the distributed systems and algorithms that we use in order to train large models quickly, and demonstrate TensorFlow (tensorflow.org), an open-source software system we have put together that makes it easy to conduct research in large-scale machine learning.

Monday December 7, 2015 09:30 - 11:30

Level 2 room 210 E,F

Level 2 room 210 E,F

Monte Carlo Inference Methods

"Monte Carlo" methods use random sampling to understand a system,

estimate averages, or compute integrals. Monte Carlo methods were

amongst the earliest applications run on electronic computers in the

1940s, and continue to see widespread use and research as our models and

computational power grow. In the NIPS community, random sampling is

widely used within optimization methods, and as a way to perform

inference in probabilistic models. Here "inference" simply means

obtaining multiple plausible settings of model parameters that could

have led to the observed data. Obtaining a range of explanations tells

us both what we can and cannot know from our data, and prevents us from

making overconfident (wrong) predictions.

This introductory-level tutorial will describe some of the fundamental

Monte Carlo algorithms, and examples of how they can be combined with

models in different ways. We'll see that Monte Carlo methods are

sometimes a quick and easy way to perform inference in a new model, but

also what can go wrong, and some treatment of how to debug these

randomized algorithms.

estimate averages, or compute integrals. Monte Carlo methods were

amongst the earliest applications run on electronic computers in the

1940s, and continue to see widespread use and research as our models and

computational power grow. In the NIPS community, random sampling is

widely used within optimization methods, and as a way to perform

inference in probabilistic models. Here "inference" simply means

obtaining multiple plausible settings of model parameters that could

have led to the observed data. Obtaining a range of explanations tells

us both what we can and cannot know from our data, and prevents us from

making overconfident (wrong) predictions.

This introductory-level tutorial will describe some of the fundamental

Monte Carlo algorithms, and examples of how they can be combined with

models in different ways. We'll see that Monte Carlo methods are

sometimes a quick and easy way to perform inference in a new model, but

also what can go wrong, and some treatment of how to debug these

randomized algorithms.

Monday December 7, 2015 13:00 - 15:00

Level 2 room 210 AB

Level 2 room 210 AB

Probabilistic Programming

Probabilistic programming is a general-purpose means of expressing and automatically performing model-based inference. A key characteristic of many probabilistic programming systems is that models can be compactly expressed in terms of executable generative procedures, rather than in declarative mathematical notation. For this reason, along with automated or programmable inference, probabilistic programming has the potential to increase the number of people who can build and understand their own models. It also could make the development and testing of new general-purpose inference algorithms more efficient, and could accelerate the exploration and development of new models for application-specific use.

The primary goals of this tutorial will be to introduce probabilistic programming both as a general concept and in terms of how current systems work, to examine the historical academic context in which probabilistic programming arose, and to expose some challenges unique to probabilistic programming.

The primary goals of this tutorial will be to introduce probabilistic programming both as a general concept and in terms of how current systems work, to examine the historical academic context in which probabilistic programming arose, and to expose some challenges unique to probabilistic programming.

Monday December 7, 2015 13:00 - 15:00

Level 2 room 210 E,F

Level 2 room 210 E,F

High-Performance Hardware for Machine Learning

This tutorial will survey the state of the art in high-performance hardware for machine learning with an emphasis on hardware for training and deployment of deep neural networks (DNNs). We establish a baseline by characterizing the performance and efficiency (perf/W) of DNNs implemented on conventional CPUs. GPU implementations of DNNs make substantial improvements over this baseline. GPU implementations perform best with moderate batch sizes. We examine the sensitivity of performance to batch size. Training of DNNs can be accelerated further using both model and data parallelism, at the cost of inter-processor communication. We examine common parallel formulations and the communication traffic they induce. Training and deployment can also be accelerated by using reduced precision for weights and activations. We will examine the tradeoff between accuracy and precision in these networks. We close with a discussion of dedicated hardware for machine learning. We survey recent publications on this topic and make some general observations about the relative importance of arithmetic and memory bandwidth in such dedicated hardware.

Monday December 7, 2015 15:30 - 17:30

Level 2 room 210 E,F

Level 2 room 210 E,F

Introduction to Reinforcement Learning with Function Approximation

Reinforcement learning is a body of theory and techniques for optimal sequential decision making developed in the last thirty years primarily within the machine learning and operations research communities, and which has separately become important in psychology and neuroscience. This tutorial will develop an intuitive understanding of the underlying formal problem (Markov decision processes) and its core solution methods, including dynamic programming, Monte Carlo methods, and temporal-difference learning. It will focus on how these methods have been combined with parametric function approximation, including deep learning, to find good approximate solutions to problems that are otherwise too large to be addressed at all. Finally, it will briefly survey some recent developments in function approximation, eligibility traces, and off-policy learning.

Monday December 7, 2015 15:30 - 17:30

Level 2 room 210 AB

Level 2 room 210 AB

3D Object Proposals for Accurate Object Class Detection

The goal of this paper is to generate high-quality 3D object proposals in the context of autonomous driving. Our method exploits stereo imagery to place proposals in the form of 3D bounding boxes. We formulate the problem as minimizing an energy function encoding object size priors, ground plane as well as several depth informed features that reason about free space, point cloud densities and distance to the ground. Our experiments show significant performance gains over existing RGB and RGB-D object proposal methods on the challenging KITTI benchmark. Combined with convolutional neural net (CNN) scoring, our approach outperforms all existing results on all three KITTI object classes.

Monday December 7, 2015 19:00 - 23:59

210 C #12

210 C #12

A Bayesian Framework for Modeling Confidence in Perceptual Decision Making

The degree of confidence in one's choice or decision is a critical aspect of perceptual decision making. Attempts to quantify a decision maker's confidence by measuring accuracy in a task have yielded limited success because confidence and accuracy are typically not equal. In this paper, we introduce a Bayesian framework to model confidence in perceptual decision making. We show that this model, based on partially observable Markov decision processes (POMDPs), is able to predict confidence of a decision maker based only on the data available to the experimenter. We test our model on two experiments on confidence-based decision making involving the well-known random dots motion discrimination task. In both experiments, we show that our model's predictions closely match experimental data. Additionally, our model is also consistent with other phenomena such as the hard-easy effect in perceptual decision making.

Monday December 7, 2015 19:00 - 23:59

210 C #27

210 C #27

A class of network models recoverable by spectral clustering

Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative model for graphs with "communities" for which, because of its simplicity, the theoretical understanding has advanced fast in recent years. In particular, there have been various results showing that simple versions of spectralclustering using the Normalized Laplacian of the graph can recoverthe communities almost perfectly with high probability. Here we show that essentially the same algorithm used for the SBM and for its extension called Degree-Corrected SBM, works on a wider class of Block-Models, which we call Preference Frame Models, with essentially the same guarantees. Moreover, the parametrization we introduce clearly exhibits the free parameters needed to specify this class of models, and results in bounds that expose with more clarity the parameters that control the recovery error in this model class.

Monday December 7, 2015 19:00 - 23:59

210 C #76

210 C #76

A Nonconvex Optimization Framework for Low Rank Matrix Estimation

We study the estimation of low rank matrices via nonconvex optimization. Compared with convex relaxation, nonconvex optimization exhibits superior empirical performance for large scale instances of low rank matrix estimation. However, the understanding of its theoretical guarantees are limited. In this paper, we define the notion of projected oracle divergence based on which we establish sufficient conditions for the success of nonconvex optimization. We illustrate the consequences of this general framework for matrix sensing and completion. In particular, we prove that a broad class of nonconvex optimization algorithms, including alternating minimization and gradient-type methods, geometrically converge to the global optimum and exactly recover the true low rank matrices under standard conditions.

Monday December 7, 2015 19:00 - 23:59

210 C #101

210 C #101

A Recurrent Latent Variable Model for Sequential Data

In this paper, we explore the inclusion of latent random variables into the hidden state of a recurrent neural network (RNN) by combining the elements of the variational autoencoder. We argue that through the use of high-level latent random variables, the variational RNN (VRNN) can model the kind of variability observed in highly structured sequential data such as natural speech. We empirically evaluate the proposed model against other related sequential models on four speech datasets and one handwriting dataset. Our results show the important roles that latent random variables can play in the RNN dynamics.

Monday December 7, 2015 19:00 - 23:59

210 C #21

210 C #21

A Theory of Decision Making Under Dynamic Context

The dynamics of simple decisions are well understood and modeled as a class of random walk models (e.g. Laming, 1968; Ratcliff, 1978; Busemeyer and Townsend, 1993; Usher and McClelland, 2001; Bogacz et al., 2006). However, most real-life decisions include a rich and dynamically-changing influence of additional information we call context. In this work, we describe a computational theory of decision making under dynamically shifting context. We show how the model generalizes the dominant existing model of fixed-context decision making (Ratcliff, 1978) and can be built up from a weighted combination of fixed-context decisions evolving simultaneously. We also show how the model generalizes re- cent work on the control of attention in the Flanker task (Yu et al., 2009). Finally, we show how the model recovers qualitative data patterns in another task of longstanding psychological interest, the AX Continuous Performance Test (Servan-Schreiber et al., 1996), using the same model parameters.

Monday December 7, 2015 19:00 - 23:59

210 C #18

210 C #18

Accelerated Proximal Gradient Methods for Nonconvex Programming

Nonconvex and nonsmooth problems have recently received considerable attention in signal/image processing, statistics and machine learning. However, solving the nonconvex and nonsmooth optimization problems remains a big challenge. Accelerated proximal gradient (APG) is an excellent method for convex programming. However, it is still unknown whether the usual APG can ensure the convergence to a critical point in nonconvex programming. To address this issue, we introduce a monitor-corrector step and extend APG for general nonconvex and nonsmooth programs. Accordingly, we propose a monotone APG and a non-monotone APG. The latter waives the requirement on monotonic reduction of the objective function and needs less computation in each iteration. To the best of our knowledge, we are the first to provide APG-type algorithms for general nonconvex and nonsmooth problems ensuring that every accumulation point is a critical point, and the convergence rates remain $O(1/k^2)$ when the problems are convex, in which k is the number of iterations. Numerical results testify to the advantage of our algorithms in speed.

Monday December 7, 2015 19:00 - 23:59

210 C #96

210 C #96

Adaptive Primal-Dual Splitting Methods for Statistical Learning and Image Processing

The alternating direction method of multipliers (ADMM) is an important tool for solving complex optimization problems, but it involves minimization sub-steps that are often difficult to solve efficiently. The Primal-Dual Hybrid Gradient (PDHG) method is a powerful alternative that often has simpler substeps than ADMM, thus producing lower complexity solvers. Despite the flexibility of this method, PDHG is often impractical because it requires the careful choice of multiple stepsize parameters. There is often no intuitive way to choose these parameters to maximize efficiency, or even achieve convergence. We propose self-adaptive stepsize rules that automatically tune PDHG parameters for optimal convergence. We rigorously analyze our methods, and identify convergence rates. Numerical experiments show that adaptive PDHG has strong advantages over non-adaptive methods in terms of both efficiency and simplicity for the user.

Monday December 7, 2015 19:00 - 23:59

210 C #91

210 C #91

Adversarial Prediction Games for Multivariate Losses

Multivariate loss functions are used to assess performance in many modern prediction tasks, including information retrieval and ranking applications. Convex approximations are typically optimized in their place to avoid NP-hard empirical risk minimization problems. We propose to approximate the training data instead of the loss function by posing multivariate prediction as an adversarial game between a loss-minimizing prediction player and a loss-maximizing evaluation player constrained to match specified properties of training data. This avoids the non-convexity of empirical risk minimization, but game sizes are exponential in the number of predicted variables. We overcome this intractability using the double oracle constraint generation method. We demonstrate the efficiency and predictive performance of our approach on tasks evaluated using the precision at k, the F-score and the discounted cumulative gain.

Monday December 7, 2015 19:00 - 23:59

210 C #54

210 C #54

An Active Learning Framework using Sparse-Graph Codes for Sparse Polynomials and Graph Sketching

Let $f: \{-1,1\}^n \rightarrow \mathbb{R}$ be an $n$-variate polynomial consisting of $2^n$ monomials, in which only $s\ll 2^n$ coefficients are non-zero. The goal is to learn the polynomial by querying the values of $f$. We introduce an active learning framework that is associated with a low query cost and computational runtime. The significant savings are enabled by leveraging sampling strategies based on modern coding theory, specifically, the design and analysis of {\it sparse-graph codes}, such as Low-Density-Parity-Check (LDPC) codes, which represent the state-of-the-art of modern packet communications. More significantly, we show how this design perspective leads to exciting, and to the best of our knowledge, largely unexplored intellectual connections between learning and coding. The key is to relax the worst-case assumption with an ensemble-average setting, where the polynomial is assumed to be drawn uniformly at random from the ensemble of all polynomials (of a given size $n$ and sparsity $s$). Our framework succeeds with high probability with respect to the polynomial ensemble with sparsity up to $s={O}(2^{\delta n})$ for any $\delta\in(0,1)$, where $f$ is exactly learned using ${O}(ns)$ queries in time ${O}(n s \log s)$, even if the queries are perturbed by Gaussian noise. We further apply the proposed framework to graph sketching, which is the problem of inferring sparse graphs by querying graph cuts. By writing the cut function as a polynomial and exploiting the graph structure, we propose a sketching algorithm to learn the an arbitrary $n$-node unknown graph using only few cut queries, which scales {\it almost linearly} in the number of edges and {\it sub-linearly} in the graph size $n$. Experiments on real datasets show significant reductions in the runtime and query complexity compared with competitive schemes.

Monday December 7, 2015 19:00 - 23:59

210 C #65

210 C #65

Anytime Influence Bounds and the Explosive Behavior of Continuous-Time Diffusion Networks

The paper studies transition phenomena in information cascades observed along a diffusion process over some graph. We introduce the Laplace Hazard matrix and show that its spectral radius fully characterizes the dynamics of the contagion both in terms of influence and of explosion time. Using this concept, we prove tight non-asymptotic bounds for the influence of a set of nodes, and we also provide an in-depth analysis of the critical time after which the contagion becomes super-critical. Our contributions include formal definitions and tight lower bounds of critical explosion time. We illustrate the relevance of our theoretical results through several examples of information cascades used in epidemiology and viral marketing models. Finally, we provide a series of numerical experiments for various types of networks which confirm the tightness of the theoretical bounds.

Monday December 7, 2015 19:00 - 23:59

210 C #69

210 C #69

Are You Talking to a Machine? Dataset and Methods for Multilingual Image Question

In this paper, we present the mQA model, which is able to answer questions about the content of an image. The answer can be a sentence, a phrase or a single word. Our model contains four components: a Long Short-Term Memory (LSTM) to extract the question representation, a Convolutional Neural Network (CNN) to extract the visual representation, an LSTM for storing the linguistic context in an answer, and a fusing component to combine the information from the first three components and generate the answer. We construct a Freestyle Multilingual Image Question Answering (FM-IQA) dataset to train and evaluate our mQA model. It contains over 150,000 images and 310,000 freestyle Chinese question-answer pairs and their English translations. The quality of the generated answers of our mQA model on this dataset is evaluated by human judges through a Turing Test. Specifically, we mix the answers provided by humans and our model. The human judges need to distinguish our model from the human. They will also provide a score (i.e. 0, 1, 2, the larger the better) indicating the quality of the answer. We propose strategies to monitor the quality of this evaluation process. The experiments show that in 64.7% of cases, the human judges cannot distinguish our model from humans. The average score is 1.454 (1.918 for human). The details of this work, including the FM-IQA dataset, can be found on the project page: \url{http://idl.baidu.com/FM-IQA.html}.

Monday December 7, 2015 19:00 - 23:59

210 C #9

210 C #9

BACKSHIFT: Learning causal cyclic graphs from unknown shift interventions

We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions (``shift interventions''). The location and strength of these interventions do not have to be known and can be estimated from the data. Our method, called BACKSHIFT, only uses second moments of the data and performs simple joint matrix diagonalization, applied to differences between covariance matrices. We give a sufficient and necessary condition for identifiability of the system, which is fulfilled almost surely under some quite general assumptions if and only if there are at least three distinct experimental settings, one of which can be pure observational data. We demonstrate the performance on some simulated data and applications in flow cytometry and financial time series.

Monday December 7, 2015 19:00 - 23:59

210 C #50

210 C #50

Bandits with Unobserved Confounders: A Causal Approach

The Multi-Armed Bandit problem constitutes an archetypal setting for sequential decision-making, permeating multiple domains including engineering, business, and medicine. One of the hallmarks of a bandit setting is the agent's capacity to explore its environment through active intervention, which contrasts with the ability to collect passive data by estimating associational relationships between actions and payouts. The existence of unobserved confounders, namely unmeasured variables affecting both the action and the outcome variables, implies that these two data-collection modes will in general not coincide. In this paper, we show that formalizing this distinction has conceptual and algorithmic implications to the bandit setting. The current generation of bandit algorithms implicitly try to maximize rewards based on estimation of the experimental distribution, which we show is not always the best strategy to pursue. Indeed, to achieve low regret in certain realistic classes of bandit problems (namely, in the face of unobserved confounders), both experimental and observational quantities are required by the rational agent. After this realization, we propose an optimization metric (employing both experimental and observational distributions) that bandit agents should pursue, and illustrate its benefits over traditional algorithms.

Monday December 7, 2015 19:00 - 23:59

210 C #60

210 C #60

Basis refinement strategies for linear value function approximation in MDPs

We provide a theoretical framework for analyzing basis function construction for linear value function approximation in Markov Decision Processes (MDPs). We show that important existing methods, such as Krylov bases and Bellman-error-based methods are a special case of the general framework we develop. We provide a general algorithmic framework for computing basis function refinements which “respect” the dynamics of the environment, and we derive approximation error bounds that apply for any algorithm respecting this general framework. We also show how, using ideas related to bisimulation metrics, one can translate basis refinement into a process of finding “prototypes” that are diverse enough to represent the given MDP.

Monday December 7, 2015 19:00 - 23:59

210 C #62

210 C #62

Bayesian Optimization with Exponential Convergence

This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the delta-cover sampling. Most Bayesian optimization methods require auxiliary optimization: an additional non-convex global optimization problem, which can be time-consuming and hard to implement in practice. Also, the existing Bayesian optimization method with exponential convergence requires access to the delta-cover sampling, which was considered to be impractical. Our approach eliminates both requirements and achieves an exponential convergence rate.

Monday December 7, 2015 19:00 - 23:59

210 C #83

210 C #83

Bidirectional Recurrent Neural Networks as Generative Models

Bidirectional recurrent neural networks (RNN) are trained to predict both in the positive and negative time directions simultaneously. They have not been used commonly in unsupervised tasks, because a probabilistic interpretation of the model has been difficult. Recently, two different frameworks, GSN and NADE, provide a connection between reconstruction and probabilistic modeling, which makes the interpretation possible. As far as we know, neither GSN or NADE have been studied in the context of time series before.As an example of an unsupervised task, we study the problem of filling in gaps in high-dimensional time series with complex dynamics. Although unidirectional RNNs have recently been trained successfully to model such time series, inference in the negative time direction is non-trivial. We propose two probabilistic interpretations of bidirectional RNNs that can be used to reconstruct missing gaps efficiently. Our experiments on text data show that both proposed methods are much more accurate than unidirectional reconstructions, although a bit less accurate than a computationally complex bidirectional Bayesian inference on the unidirectional RNN. We also provide results on music data for which the Bayesian inference is computationally infeasible, demonstrating the scalability of the proposed methods.

Monday December 7, 2015 19:00 - 23:59

210 C #19

210 C #19

BinaryConnect: Training Deep Neural Networks with binary weights during propagations

Deep Neural Networks (DNN) have achieved state-of-the-art results in a wide range of tasks, with the best results obtained with large training sets and large models. In the past, GPUs enabled these breakthroughs because of their greater computational speed. In the future, faster computation at both training and test time is likely to be crucial for further progress and for consumer applications on low-power devices. As a result, there is much interest in research and development of dedicated hardware for Deep Learning (DL). Binary weights, i.e., weights which are constrained to only two possible values (e.g. -1 or 1), would bring great benefits to specialized DL hardware by replacing many multiply-accumulate operations by simple accumulations, as multipliers are the most space and power-hungry components of the digital implementation of neural networks. We introduce BinaryConnect, a method which consists in training a DNN with binary weights during the forward and backward propagations, while retaining precision of the stored weights in which gradients are accumulated. Like other dropout schemes, we show that BinaryConnect acts as regularizer and we obtain near state-of-the-art results with BinaryConnect on the permutation-invariant MNIST, CIFAR-10 and SVHN.

Monday December 7, 2015 19:00 - 23:59

210 C #15

210 C #15

Black-box optimization of noisy functions with unknown smoothness

We study the problem of black-box optimization of a function $f$ of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after $n$ evaluations is at most a factor of $\sqrt{\ln n}$ away from the error of the best known optimization algorithms using the knowledge of the smoothness.

Monday December 7, 2015 19:00 - 23:59

210 C #89

210 C #89

Calibrated Structured Prediction

In user-facing applications, displaying calibrated confidence measures---probabilities that correspond to true frequency---can be as important as obtaining high accuracy. We are interested in calibration for structured prediction problems such as speech recognition, optical character recognition, and medical diagnosis. Structured prediction presents new challenges for calibration: the output space is large, and users may issue many types of probability queries (e.g., marginals) on the structured output. We extend the notion of calibration so as to handle various subtleties pertaining to the structured setting, and then provide a simple recalibration method that trains a binary classifier to predict probabilities of interest. We explore a range of features appropriate for structured recalibration, and demonstrate their efficacy on three real-world datasets.

Monday December 7, 2015 19:00 - 23:59

210 C #26

210 C #26

Combinatorial Cascading Bandits

We propose combinatorial cascading bandits, a class of partial monitoring problems where at each step a learning agent chooses a tuple of ground items subject to constraints and receives a reward if and only if the weights of all chosen items are one. The weights of the items are binary, stochastic, and drawn independently of each other. The agent observes the index of the first chosen item whose weight is zero. This observation model arises in network routing, for instance, where the learning agent may only observe the first link in the routing path which is down, and blocks the path. We propose a UCB-like algorithm for solving our problems, CombCascade; and prove gap-dependent and gap-free upper bounds on its n-step regret. Our proofs build on recent work in stochastic combinatorial semi-bandits but also address two novel challenges of our setting, a non-linear reward function and partial observability. We evaluate CombCascade on two real-world problems and show that it performs well even when our modeling assumptions are violated. We also demonstrate that our setting requires a new learning algorithm.

Monday December 7, 2015 19:00 - 23:59

210 C #90

210 C #90

Communication Complexity of Distributed Convex Learning and Optimization

We study the fundamental limits to communication-efficient distributed methods for convex learning and optimization, under different assumptions on the information available to individual machines, and the types of functions considered. We identify cases where existing algorithms are already worst-case optimal, as well as cases where room for further improvement is still possible. Among other things, our results indicate that without similarity between the local objective functions (due to statistical data similarity or otherwise) many communication rounds may be required, even if the machines have unbounded computational power.

Monday December 7, 2015 19:00 - 23:59

210 C #99

210 C #99

Convergence Analysis of Prediction Markets via Randomized Subspace Descent

Prediction markets are economic mechanisms for aggregating information about future events through sequential interactions with traders. The pricing mechanisms in these markets are known to be related to optimization algorithms in machine learning and through these connections we have some understanding of how equilibrium market prices relate to the beliefs of the traders in a market. However, little is known about rates and guarantees for the convergence of these sequential mechanisms, and two recent papers cite this as an important open question.In this paper we show how some previously studied prediction market trading models can be understood as a natural generalization of randomized coordinate descent which we call randomized subspace descent (RSD). We establish convergence rates for RSD and leverage them to prove rates for the two prediction market models above, answering the open questions. Our results extend beyond standard centralized markets to arbitrary trade networks.

Monday December 7, 2015 19:00 - 23:59

210 C #95

210 C #95

Convolutional Neural Networks with Intra-Layer Recurrent Connections for Scene Labeling

Scene labeling is a challenging computer vision task. It requires the use of both local discriminative features and global context information. We adopt a deep recurrent convolutional neural network (RCNN) for this task, which is originally proposed for object recognition. Different from traditional convolutional neural networks (CNN), this model has intra-layer recurrent connections in the convolutional layers. Therefore each convolutional layer becomes a two-dimensional recurrent neural network. The units receive constant feed-forward inputs from the previous layer and recurrent inputs from their neighborhoods. While recurrent iterations proceed, the region of context captured by each unit expands. In this way, feature extraction and context modulation are seamlessly integrated, which is different from typical methods that entail separate modules for the two steps. To further utilize the context, a multi-scale RCNN is proposed. Over two benchmark datasets, Standford Background and Sift Flow, the model outperforms many state-of-the-art models in accuracy and efficiency.

Monday December 7, 2015 19:00 - 23:59

210 C #2

210 C #2

Copula variational inference

We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-field or structured approach. Copula variational inference has many advantages: it reduces bias; it is less sensitive to local optima; it is less sensitive to hyperparameters; and it helps characterize and interpret the dependency among the latent variables.

Monday December 7, 2015 19:00 - 23:59

210 C #37

210 C #37

Decomposition Bounds for Marginal MAP

Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and convergent variational algorithms, such as dual decomposition, exist. In this work, we generalize dual decomposition to a generic powered-sum inference task, which includes marginal MAP, along with pure marginalization and MAP, as special cases. Our method is based on a block coordinate descent algorithm on a new convex decomposition bound, that is guaranteed to converge monotonically, and can be parallelized efficiently. We demonstrate our approach on various inference queries over real-world problems from the UAI approximate inference challenge, showing that our framework is faster and more reliable than previous methods.

Monday December 7, 2015 19:00 - 23:59

210 C #68

210 C #68

Deep Knowledge Tracing

Knowledge tracing, where a machine models the knowledge of a student as they interact with coursework, is an established and significantly unsolved problem in computer supported education.In this paper we explore the benefit of using recurrent neural networks to model student learning.This family of models have important advantages over current state of the art methods in that they do not require the explicit encoding of human domain knowledge,and have a far more flexible functional form which can capture substantially more complex student interactions.We show that these neural networks outperform the current state of the art in prediction on real student data,while allowing straightforward interpretation and discovery of structure in the curriculum.These results suggest a promising new line of research for knowledge tracing.

Monday December 7, 2015 19:00 - 23:59

210 C #22

210 C #22

Deep Temporal Sigmoid Belief Networks for Sequence Modeling

Deep dynamic generative models are developed to learn sequential dependencies in time-series data. The multi-layered model is designed by constructing a hierarchy of temporal sigmoid belief networks (TSBNs), defined as a sequential stack of sigmoid belief networks (SBNs). Each SBN has a contextual hidden state, inherited from the previous SBNs in the sequence, and is used to regulate its hidden bias. Scalable learning and inference algorithms are derived by introducing a recognition model that yields fast sampling from the variational posterior. This recognition model is trained jointly with the generative model, by maximizing its variational lower bound on the log-likelihood. Experimental results on bouncing balls, polyphonic music, motion capture, and text streams show that the proposed approach achieves state-of-the-art predictive performance, and has the capacity to synthesize various sequences.

Monday December 7, 2015 19:00 - 23:59

210 C #23

210 C #23

Dependent Multinomial Models Made Easy: Stick-Breaking with the Polya-gamma Augmentation

Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cases, we expect some form of dependency between the draws: the nucleotide at one position in the DNA strand may depend on the preceding nucleotides, children's names are highly correlated from year to year, and topics in text may be correlated and dynamic. These dependencies are not naturally captured by the typical Dirichlet-multinomial formulation. Here, we leverage a logistic stick-breaking representation and recent innovations in P\'{o}lya-gamma augmentation to reformulate the multinomial distribution in terms of latent variables with jointly Gaussian likelihoods, enabling us to take advantage of a host of Bayesian inference techniques for Gaussian models with minimal overhead.

Monday December 7, 2015 19:00 - 23:59

210 C #28

210 C #28

Differentially Private Learning of Structured Discrete Distributions

We investigate the problem of learning an unknown probability distribution over a discrete population from random samples. Our goal is to design efficient algorithms that simultaneously achieve low error in total variation norm while guaranteeing Differential Privacy to the individuals of the population.We describe a general approach that yields near sample-optimal and computationally efficient differentially private estimators for a wide range of well-studied and natural distribution families. Our theoretical results show that for a wide variety of structured distributions there exist private estimation algorithms that are nearly as efficient - both in terms of sample size and running time - as their non-private counterparts. We complement our theoretical guarantees with an experimental evaluation. Our experiments illustrate the speed and accuracy of our private estimators on both synthetic mixture models and a large public data set.

Monday December 7, 2015 19:00 - 23:59

210 C #81

210 C #81

Discrete Rényi Classifiers

Consider the binary classification problem of predicting a target variable Y from a discrete feature vector X = (X1,...,Xd). When the probability distribution P(X,Y) is known, the optimal classifier, leading to the minimum misclassification rate, is given by the Maximum A-posteriori Probability (MAP) decision rule. However, in practice, estimating the complete joint distribution P(X,Y) is computationally and statistically impossible for large values of d. Therefore, an alternative approach is to first estimate some low order marginals of the joint probability distribution P(X,Y) and then design the classifier based on the estimated low order marginals. This approach is also helpful when the complete training data instances are not available due to privacy concerns. In this work, we consider the problem of designing the optimum classifier based on some estimated low order marginals of (X,Y). We prove that for a given set of marginals, the minimum Hirschfeld-Gebelein-R´enyi (HGR) correlation principle introduced in [1] leads to a randomized classification rule which is shown to have a misclassification rate no larger than twice the misclassification rate of the optimal classifier. Then, we show that under a separability condition, the proposed algorithm is equivalent to a randomized linear regression approach which naturally results in a robust feature selection method selecting a subset of features having the maximum worst case HGR correlation with the target variable. Our theoretical upper-bound is similar to the recent Discrete Chebyshev Classifier (DCC) approach [2], while the proposed algorithm has significant computational advantages since it only requires solving a least square optimization problem. Finally, we numerically compare our proposed algorithm with the DCC classifier and show that the proposed algorithm results in better misclassification rate over various UCI data repository datasets.

Monday December 7, 2015 19:00 - 23:59

210 C #66

210 C #66

Double or Nothing: Multiplicative Incentive Mechanisms for Crowdsourcing

Crowdsourcing has gained immense popularity in machine learning applications for obtaining large amounts of labeled data. Crowdsourcing is cheap and fast, but suffers from the problem of low-quality data. To address this fundamental challenge in crowdsourcing, we propose a simple payment mechanism to incentivize workers to answer only the questions that they are sure of and skip the rest. We show that surprisingly, under a mild and natural "no-free-lunch" requirement, this mechanism is the one and only incentive-compatible payment mechanism possible. We also show that among all possible incentive-compatible mechanisms (that may or may not satisfy no-free-lunch), our mechanism makes the smallest possible payment to spammers. Interestingly, this unique mechanism takes a "multiplicative" form. The simplicity of the mechanism is an added benefit. In preliminary experiments involving over several hundred workers, we observe a significant reduction in the error rates under our unique mechanism for the same or lower monetary expenditure.

Monday December 7, 2015 19:00 - 23:59

210 C #45

210 C #45

Embedding Inference for Structured Multilabel Prediction

A key bottleneck in structured output prediction is the need for inference during training and testing, usually requiring some form of dynamic programming. Rather than using approximate inference or tailoring a specialized inference method for a particular structure---standard responses to the scaling challenge---we propose to embed prediction constraints directly into the learned representation. By eliminating the need for explicit inference a more scalable approach to structured output prediction can be achieved, particularly at test time. We demonstrate the idea for multi-label prediction under subsumption and mutual exclusion constraints, where a relationship to maximum margin structured output prediction can be established. Experiments demonstrate that the benefits of structured output training can still be realized even after inference has been eliminated.

Monday December 7, 2015 19:00 - 23:59

210 C #43

210 C #43

Estimating Mixture Models via Mixtures of Polynomials

Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates are easy to derive for a wide class of mixture models. However, the likelihood of a mixture model is non-convex, so EM has no known global convergence guarantees. Recently, method of moments approaches offer global guarantees for some mixture models, but they do not extend easily to the range of mixture models that exist. In this work, we present Polymom, an unifying framework based on method of moments in which estimation procedures are easily derivable, just as in EM. Polymom is applicable when the moments of a single mixture component are polynomials of the parameters. Our key observation is that the moments of the mixture model are a mixture of these polynomials, which allows us to cast estimation as a Generalized Moment Problem. We solve its relaxations using semidefinite optimization, and then extract parameters using ideas from computer algebra. This framework allows us to draw insights and apply tools from convex optimization, computer algebra and the theory of moments to study problems in statistical estimation. Simulations show good empirical performance on several models.

Monday December 7, 2015 19:00 - 23:59

210 C #70

210 C #70

Expectation Particle Belief Propagation

We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions approximating the local beliefs at each note of the MRF. This is achieved by considering proposal distributions in the exponential family whose parameters are updated iterately in an Expectation Propagation (EP) framework. The proposed particle scheme provides consistent estimation of the LBP marginals as the number of particles increases. We demonstrate that it provides more accurate results than the Particle Belief Propagation (PBP) algorithm of Ihler and McAllester (2009) at a fraction of the computational cost and is additionally more robust empirically. The computational complexity of our algorithm at each iteration is quadratic in the number of particles. We also propose an accelerated implementation with sub-quadratic computational complexity which still provides consistent estimates of the loopy BP marginal distributions and performs almost as well as the original procedure.

Monday December 7, 2015 19:00 - 23:59

210 C #42

210 C #42

Explore no more: Improved high-probability regret bounds for non-stochastic bandits

This work addresses the problem of regret minimization in non-stochastic multi-armed bandit problems, focusing on performance guarantees that hold with high probability. Such results are rather scarce in the literature since proving them requires a large deal of technical effort and significant modifications to the standard, more intuitive algorithms that come only with guarantees that hold on expectation. One of these modifications is forcing the learner to sample arms from the uniform distribution at least $\Omega(\sqrt{T})$ times over $T$ rounds, which can adversely affect performance if many of the arms are suboptimal. While it is widely conjectured that this property is essential for proving high-probability regret bounds, we show in this paper that it is possible to achieve such strong results without this undesirable exploration component. Our result relies on a simple and intuitive loss-estimation strategy called Implicit eXploration (IX) that allows a remarkably clean analysis. To demonstrate the flexibility of our technique, we derive several improved high-probability bounds for various extensions of the standard multi-armed bandit framework.Finally, we conduct a simple experiment that illustrates the robustness of our implicit exploration technique.

Monday December 7, 2015 19:00 - 23:59

210 C #100

210 C #100

Exploring Models and Data for Image Question Answering

This work aims to address the problem of image-based question-answering (QA) with new models and datasets. In our work, we propose to use neural networks and visual semantic embeddings, without intermediate stages such as object detection and image segmentation, to predict answers to simple questions about images. Our model performs 1.8 times better than the only published results on an existing image QA dataset. We also present a question generation algorithm that converts image descriptions, which are widely available, into QA form. We used this algorithm to produce an order-of-magnitude larger dataset, with more evenly distributed answers. A suite of baseline results on this new dataset are also presented.

Monday December 7, 2015 19:00 - 23:59

210 C #8

210 C #8

Fast and Accurate Inference of Plackett–Luce Models

We show that the maximum-likelihood (ML) estimate of models derived from Luce's choice axiom (e.g., the Plackett-Luce model) can be expressed as the stationary distribution of a Markov chain. This conveys insight into several recently proposed spectral inference algorithms. We take advantage of this perspective and formulate a new spectral algorithm that is significantly more accurate than previous ones for the Plackett--Luce model. With a simple adaptation, this algorithm can be used iteratively, producing a sequence of estimates that converges to the ML estimate. The ML version runs faster than competing approaches on a benchmark of five datasets. Our algorithms are easy to implement, making them relevant for practitioners at large.

Monday December 7, 2015 19:00 - 23:59

210 C #49

210 C #49

Fast Randomized Kernel Ridge Regression with Statistical Guarantees

One approach to improving the running time of kernel-based methods is to build a small sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guarantees on its statistical performance.By extending the notion of \emph{statistical leverage scores} to the setting of kernel ridge regression, we are able to identify a sampling distribution that reduces the size of the sketch (i.e., the required number of columns to be sampled) to the \emph{effective dimensionality} of the problem. This latter quantity is often much smaller than previous bounds that depend on the \emph{maximal degrees of freedom}. We give an empirical evidence supporting this fact. Our second contribution is to present a fast algorithm to quickly compute coarse approximations to thesescores in time linear in the number of samples. More precisely, the running time of the algorithm is $O(np^2)$ with $p$ only depending on the trace of the kernel matrix and the regularization parameter. This is obtained via a variant of squared length sampling that we adapt to the kernel setting. Lastly, we discuss how this new notion of the leverage of a data point captures a fine notion of the difficulty of the learning problem.

Monday December 7, 2015 19:00 - 23:59

210 C #84

210 C #84

Fast Second Order Stochastic Backpropagation for Variational Inference

We propose a second-order (Hessian or Hessian-free) based optimization method for variational inference inspired by Gaussian backpropagation, and argue that quasi-Newton optimization can be developed as well. This is accomplished by generalizing the gradient computation in stochastic backpropagation via a reparametrization trick with lower complexity. As an illustrative example, we apply this approach to the problems of Bayesian logistic regression and variational auto-encoder (VAE). Additionally, we compute bounds on the estimator variance of intractable expectations for the family of Lipschitz continuous function. Our method is practical, scalable and model free. We demonstrate our method on several real-world datasets and provide comparisons with other stochastic gradient methods to show substantial enhancement in convergence rates.

Monday December 7, 2015 19:00 - 23:59

210 C #38

210 C #38

Fast Two-Sample Testing with Analytic Representations of Probability Measures

We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses smoothed empirical characteristic functions to represent the distributions, the second uses distribution embeddings in a reproducing kernel Hilbert space. Analyticity implies that differences in the distributions may be detected almost surely at a finite number of randomly chosen locations/frequencies. The new tests are consistent against a larger class of alternatives than the previous linear-time tests based on the (non-smoothed) empirical characteristic functions, while being much faster than the current state-of-the-art quadratic-time kernel-based or energy distance-based tests. Experiments on artificial benchmarks and on challenging real-world testing problems demonstrate that our tests give a better power/time tradeoff than competing approaches, and in some cases, better outright power than even the most expensive quadratic-time tests. This performance advantage is retained even in high dimensions, and in cases where the difference in distributions is not observable with low order statistics.

Monday December 7, 2015 19:00 - 23:59

210 C #53

210 C #53

Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks

State-of-the-art object detection networks depend on region proposal algorithms to hypothesize object locations. Advances like SPPnet and Fast R-CNN have reduced the running time of these detection networks, exposing region proposal computation as a bottleneck. In this work, we introduce a Region Proposal Network (RPN) that shares full-image convolutional features with the detection network, thus enabling nearly cost-free region proposals. An RPN is a fully-convolutional network that simultaneously predicts object bounds and objectness scores at each position. RPNs are trained end-to-end to generate high-quality region proposals, which are used by Fast R-CNN for detection. With a simple alternating optimization, RPN and Fast R-CNN can be trained to share convolutional features. For the very deep VGG-16 model, our detection system has a frame rate of 5fps (including all steps) on a GPU, while achieving state-of-the-art object detection accuracy on PASCAL VOC 2007 (73.2% mAP) and 2012 (70.4% mAP) using 300 proposals per image. Code is available at https://github.com/ShaoqingRen/faster_rcnn.

Monday December 7, 2015 19:00 - 23:59

210 C #6

210 C #6

GAP Safe screening rules for sparse multi-task and multi-class models

High dimensional regression benefits from sparsity promoting regularizations. Screening rules leverage the known sparsity of the solution by ignoring some variables in the optimization, hence speeding up solvers. When the procedure is proven not to discard features wrongly the rules are said to be safe. In this paper we derive new safe rules for generalized linear models regularized with L1 and L1/L2 norms. The rules are based on duality gap computations and spherical safe regions whose diameters converge to zero. This allows to discard safely more variables, in particular for low regularization parameters. The GAP Safe rule can cope with any iterative solver and we illustrate its performance on coordinate descent for multi-task Lasso, binary and multinomial logistic regression, demonstrating significant speed ups on all tested datasets with respect to previous safe rules.

Monday December 7, 2015 19:00 - 23:59

210 C #67

210 C #67

Generative Image Modeling Using Spatial LSTMs

Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a number of problems but only recently have found their way into generative image models. We here introduce a recurrent image model based on multi-dimensional long short-term memory units which are particularly suited for image modeling due to their spatial structure. Our model scales to images of arbitrary size and its likelihood is computationally tractable. We find that it outperforms the state of the art in quantitative comparisons on several image datasets and produces promising results when used for texture synthesis and inpainting.

Monday December 7, 2015 19:00 - 23:59

210 C #5

210 C #5

Grammar as a Foreign Language

Syntactic constituency parsing is a fundamental problem in naturallanguage processing which has been the subject of intensive researchand engineering for decades. As a result, the most accurate parsersare domain specific, complex, and inefficient. In this paper we showthat the domain agnostic attention-enhanced sequence-to-sequence modelachieves state-of-the-art results on the most widely used syntacticconstituency parsing dataset, when trained on a large synthetic corpusthat was annotated using existing parsers. It also matches theperformance of standard parsers when trained on a smallhuman-annotated dataset, which shows that this model is highlydata-efficient, in contrast to sequence-to-sequence models without theattention mechanism. Our parser is also fast, processing over ahundred sentences per second with an unoptimized CPU implementation.

Monday December 7, 2015 19:00 - 23:59

210 C #3

210 C #3

Halting in Random Walk Kernels

Random walk kernels measure graph similarity by counting matching walks in two graphs. In their most popular form of geometric random walk kernels, longer walks of length $k$ are downweighted by a factor of $\lambda^k$ ($\lambda < 1$) to ensure convergence of the corresponding geometric series. We know from the field of link prediction that this downweighting often leads to a phenomenon referred to as halting: Longer walks are downweighted so much that the similarity score is completely dominated by the comparison of walks of length 1. This is a naive kernel between edges and vertices. We theoretically show that halting may occur in geometric random walk kernels. We also empirically quantify its impact in simulated datasets and popular graph classification benchmark datasets. Our findings promise to be instrumental in future graph kernel development and applications of random walk kernels.

Monday December 7, 2015 19:00 - 23:59

210 C #56

210 C #56

Hessian-free Optimization for Learning Deep Multidimensional Recurrent Neural Networks

Multidimensional recurrent neural networks (MDRNNs) have shown a remarkable performance in the area of speech and handwriting recognition. The performance of an MDRNN is improved by further increasing its depth, and the difficulty of learning the deeper network is overcome by using Hessian-free (HF) optimization. Given that connectionist temporal classification (CTC) is utilized as an objective of learning an MDRNN for sequence labeling, the non-convexity of CTC poses a problem when applying HF to the network. As a solution, a convex approximation of CTC is formulated and its relationship with the EM algorithm and the Fisher information matrix is discussed. An MDRNN up to a depth of 15 layers is successfully trained using HF, resulting in an improved performance for sequence labeling.

Monday December 7, 2015 19:00 - 23:59

210 C #32

210 C #32

Hidden Technical Debt in Machine Learning Systems

Machine learning offers a fantastically powerful toolkit for building useful complexprediction systems quickly. This paper argues it is dangerous to think ofthese quick wins as coming for free. Using the software engineering frameworkof technical debt, we find it is common to incur massive ongoing maintenancecosts in real-world ML systems. We explore several ML-specific risk factors toaccount for in system design. These include boundary erosion, entanglement,hidden feedback loops, undeclared consumers, data dependencies, configurationissues, changes in the external world, and a variety of system-level anti-patterns.

Monday December 7, 2015 19:00 - 23:59

210 C #24

210 C #24

Individual Planning in Infinite-Horizon Multiagent Settings: Inference, Structure and Scalability

This paper provides the first formalization of self-interested planning in multiagent settings using expectation-maximization (EM). Our formalization in the context of infinite-horizon and finitely-nested interactive POMDPs (I-POMDP) is distinct from EM formulations for POMDPs and cooperative multiagent planning frameworks. We exploit the graphical model structure specific to I-POMDPs, and present a new approach based on block-coordinate descent for further speed up. Forward filtering-backward sampling -- a combination of exact filtering with sampling -- is explored to exploit problem structure.

Monday December 7, 2015 19:00 - 23:59

210 C #102

210 C #102

Infinite Factorial Dynamical Model

We propose the infinite factorial dynamic model (iFDM), a general Bayesian nonparametric model for source separation. Our model builds on the Markov Indian buffet process to consider a potentially unbounded number of hidden Markov chains (sources) that evolve independently according to some dynamics, in which the state space can be either discrete or continuous. For posterior inference, we develop an algorithm based on particle Gibbs with ancestor sampling that can be efficiently applied to a wide range of source separation problems. We evaluate the performance of our iFDM on four well-known applications: multitarget tracking, cocktail party, power disaggregation, and multiuser detection. Our experimental results show that our approach for source separation does not only outperform previous approaches, but it can also handle problems that were computationally intractable for existing approaches.

Monday December 7, 2015 19:00 - 23:59

210 C #35

210 C #35

Learning From Small Samples: An Analysis of Simple Decision Heuristics

Simple decision heuristics are models of human and animal behavior that use few pieces of information---perhaps only a single piece of information---and integrate the pieces in simple ways, for example, by considering them sequentially, one at a time, or by giving them equal weight. It is unknown how quickly these heuristics can be learned from experience. We show, analytically and empirically, that only a few training samples lead to substantial progress in learning. We focus on three families of heuristics: single-cue decision making, lexicographic decision making, and tallying. Our empirical analysis is the most extensive to date, employing 63 natural data sets on diverse subjects.

Monday December 7, 2015 19:00 - 23:59

210 C #11

210 C #11

Learning spatiotemporal trajectories from manifold-valued longitudinal data

We propose a Bayesian mixed-effects model to learn typical scenarios of changes from longitudinal manifold-valued data, namely repeated measurements of the same objects or individuals at several points in time. The model allows to estimate a group-average trajectory in the space of measurements. Random variations of this trajectory result from spatiotemporal transformations, which allow changes in the direction of the trajectory and in the pace at which trajectories are followed. The use of the tools of Riemannian geometry allows to derive a generic algorithm for any kind of data with smooth constraints, which lie therefore on a Riemannian manifold. Stochastic approximations of the Expectation-Maximization algorithm is used to estimate the model parameters in this highly non-linear setting.The method is used to estimate a data-driven model of the progressive impairments of cognitive functions during the onset of Alzheimer's disease. Experimental results show that the model correctly put into correspondence the age at which each individual was diagnosed with the disease, thus validating the fact that it effectively estimated a normative scenario of disease progression. Random effects provide unique insights into the variations in the ordering and timing of the succession of cognitive impairments across different individuals.

Monday December 7, 2015 19:00 - 23:59

210 C #31

210 C #31

Learning to Transduce with Unbounded Memory

Recently, strong results have been demonstrated by Deep Recurrent Neural Networks on natural language transduction problems. In this paper we explore the representational power of these models using synthetic grammars designed to exhibit phenomena similar to those found in real transduction problems such as machine translation. These experiments lead us to propose new memory-based recurrent networks that implement continuously differentiable analogues of traditional data structures such as Stacks, Queues, and DeQues. We show that these architectures exhibit superior generalisation performance to Deep RNNs and are often able to learn the underlying generating algorithms in our transduction experiments.

Monday December 7, 2015 19:00 - 23:59

210 C #16

210 C #16

Learning with a Wasserstein Loss

Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe an efficient learning algorithm based on this regularization, as well as a novel extension of the Wasserstein distance from probability measures to unnormalized measures. We also describe a statistical learning bound for the loss. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data tag prediction problem, using the Yahoo Flickr Creative Commons dataset, outperforming a baseline that doesn't use the metric.

Monday December 7, 2015 19:00 - 23:59

210 C #47

210 C #47

Learning with Relaxed Supervision

For weakly-supervised problems with deterministic constraints between the latent variables and observed output, learning necessitates performing inference over latent variables conditioned on the output, which can be intractable no matter how simple the model family is. Even finding a single latent variable setting that satisfies the constraints could be difficult; for instance, the observed output may be the result of a latent database query or graphics program which must be inferred. Here, the difficulty lies in not the model but the supervision, and poor approximations at this stage could lead to following the wrong learning signal entirely. In this paper, we develop a rigorous approach to relaxing the supervision, which yields asymptotically consistent parameter estimates despite altering the supervision. Our approach parameterizes a family of increasingly accurate relaxations, and jointly optimizes both the model and relaxation parameters, while formulating constraints between these parameters to ensure efficient inference. These efficiency constraints allow us to learn in otherwise intractable settings, while asymptotic consistency ensures that we always follow a valid learning signal.

Monday December 7, 2015 19:00 - 23:59

210 C #51

210 C #51

Lifted Symmetry Detection and Breaking for MAP Inference

Symmetry breaking is a technique for speeding up propositional satisfiability testing by adding constraints to the theory that restrict the search space while preserving satisfiability. In this work, we extend symmetry breaking to the problem of model finding in weighted and unweighted relational theories, a class of problems that includes MAP inference in Markov Logic and similar statistical-relational languages. We introduce term symmetries, which are induced by an evidence set and extend to symmetries over a relational theory. We provide the important special case of term equivalent symmetries, showing that such symmetries can be found in low-degree polynomial time. We show how to break an exponential number of these symmetries with added constraints that are linear in the size of the domain. We demonstrate the effectiveness of these techniques through experiments in two relational domains. We also discuss the connections between relational symmetry breaking and work on lifted inference in statistical-relational reasoning.

Monday December 7, 2015 19:00 - 23:59

210 C #59

210 C #59

Local Expectation Gradients for Black Box Variational Inference

We introduce local expectation gradients which is a general purpose stochastic variational inference algorithm for constructing stochastic gradients by sampling from the variational distribution. This algorithm divides the problem of estimating the stochastic gradients over multiple variational parameters into smaller sub-tasks so that each sub-task explores intelligently the most relevant part of the variational distribution. This is achieved by performing an exact expectation over the single random variable that most correlates with the variational parameter of interest resulting in a Rao-Blackwellized estimate that has low variance. Our method works efficiently for both continuous and discrete random variables. Furthermore, the proposed algorithm has interesting similarities with Gibbs sampling but at the same time, unlike Gibbs sampling, can be trivially parallelized.

Monday December 7, 2015 19:00 - 23:59

210 C #46

210 C #46

M-Statistic for Kernel Change-Point Detection

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been proposed for this task which make fewer assumptions on the distributions than traditional parametric approach. However, none of the existing kernel statistics has provided a computationally efficient way to characterize the extremal behavior of the statistic. Such characterization is crucial for setting the detection threshold, to control the significance level in the offline case as well as the average run length in the online case. In this paper we propose two related computationally efficient M-statistics for kernel-based change-point detection when the amount of background data is large. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using a new technique based on change-of-measure. Such characterization provides us accurate detection thresholds for both offline and online cases in computationally efficient manner, without the need to resort to the more expensive simulations such as bootstrapping. We show that our methods perform well in both synthetic and real world data.

Monday December 7, 2015 19:00 - 23:59

210 C #52

210 C #52

Matrix Completion from Fewer Entries: Spectral Detectability and Rank Estimation

The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank $r$ reliably from the fewest possible random entries, and performance in achieving small reconstruction error. We propose a spectral algorithm for these two tasks called MaCBetH (for Matrix Completion with the Bethe Hessian). The rank is estimated as the number of negative eigenvalues of the Bethe Hessian matrix, and the corresponding eigenvectors are used as initial condition for the minimization of the discrepancy between the estimated matrix and the revealed entries. We analyze the performance in a random matrix setting using results from the statistical mechanics of the Hopfield neural network, and show in particular that MaCBetH efficiently detects the rank $r$ of a large $n\times m$ matrix from $C(r)r\sqrt{nm}$ entries, where $C(r)$ is a constant close to $1$. We also evaluate the corresponding root-mean-square error empirically and show that MaCBetH compares favorably to other existing approaches.

Monday December 7, 2015 19:00 - 23:59

210 C #72

210 C #72

Minimax Time Series Prediction

We consider an adversarial formulation of the problem ofpredicting a time series with square loss. The aim is to predictan arbitrary sequence of vectors almost as well as the bestsmooth comparator sequence in retrospect. Our approach allowsnatural measures of smoothness such as the squared norm ofincrements. More generally, we consider a linear time seriesmodel and penalize the comparator sequence through the energy ofthe implied driving noise terms. We derive the minimax strategyfor all problems of this type and show that it can be implementedefficiently. The optimal predictions are linear in the previousobservations. We obtain an explicit expression for the regret interms of the parameters defining the problem. For typical,simple definitions of smoothness, the computation of the optimalpredictions involves only sparse matrices. In the case ofnorm-constrained data, where the smoothness is defined in termsof the squared norm of the comparator's increments, we show thatthe regret grows as $T/\sqrt{\lambda_T}$, where $T$ is the lengthof the game and $\lambda_T$ is an increasing limit on comparatorsmoothness.

Monday December 7, 2015 19:00 - 23:59

210 C #98

210 C #98

Mixed Robust/Average Submodular Partitioning: Fast Algorithms, Guarantees, and Applications

We investigate two novel mixed robust/average-case submodular data partitioning problems that we collectively call Submodular Partitioning. These problems generalize purely robust instances of the problem, namely max-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing} (SLB), and also average-case instances, that is the submodular welfare problem (SWP) and submodular multiway partition (SMP). While the robust versions have been studied in the theory community, existing work has focused on tight approximation guarantees, and the resultant algorithms are not generally scalable to large real-world applications. This contrasts the average case instances, where most of the algorithms are scalable. In the present paper, we bridge this gap, by proposing several new algorithms (including greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees comparable to the state-of-the-art. We moreover provide new scalable algorithms that apply to additive combinations of the robust and average-case objectives. We show that these problems have many applications in machine learning (ML), including data partitioning and load balancing for distributed ML, data clustering, and image segmentation. We empirically demonstrate the efficacy of our algorithms on real-world problems involving data partitioning for distributed optimization (of convex and deep neural network objectives), and also purely unsupervised image segmentation.

Monday December 7, 2015 19:00 - 23:59

210 C #74

210 C #74

Model-Based Relative Entropy Stochastic Search

Stochastic search algorithms are general black-box optimizers. Due to their ease of use and their generality, they have recently also gained a lot of attention in operations research, machine learning and policy search. Yet, these algorithms require a lot of evaluations of the objective, scale poorly with the problem dimension, are affected by highly noisy objective functions and may converge prematurely. To alleviate these problems, we introduce a new surrogate-based stochastic search approach. We learn simple, quadratic surrogate models of the objective function. As the quality of such a quadratic approximation is limited, we do not greedily exploit the learned models. The algorithm can be misled by an inaccurate optimum introduced by the surrogate. Instead, we use information theoretic constraints to bound the `distance' between the new and old data distribution while maximizing the objective function. Additionally the new method is able to sustain the exploration of the search distribution to avoid premature convergence. We compare our method with state of art black-box optimization methods on standard uni-modal and multi-modal optimization functions, on simulated planar robot tasks and a complex robot ball throwing task.The proposed method considerably outperforms the existing approaches.

Monday December 7, 2015 19:00 - 23:59

210 C #40

210 C #40

Monotone k-Submodular Function Maximization with Size Constraints

A $k$-submodular function is a generalization of a submodular function, where the input consists of $k$ disjoint subsets, instead of a single subset, of the domain.Many machine learning problems, including influence maximization with $k$ kinds of topics and sensor placement with $k$ kinds of sensors, can be naturally modeled as the problem of maximizing monotone $k$-submodular functions.In this paper, we give constant-factor approximation algorithms for maximizing monotone $k$-submodular functions subject to several size constraints.The running time of our algorithms are almost linear in the domain size.We experimentally demonstrate that our algorithms outperform baseline algorithms in terms of the solution quality.

Monday December 7, 2015 19:00 - 23:59

210 C #77

210 C #77

Nearly Optimal Private LASSO

We present a nearly optimal differentially private version of the well known LASSO estimator. Our algorithm provides privacy protection with respect to each training data item. The excess risk of our algorithm, compared to the non-private version, is $\widetilde{O}(1/n^{2/3})$, assuming all the input data has bounded $\ell_\infty$ norm. This is the first differentially private algorithm that achieves such a bound without the polynomial dependence on $p$ under no addition assumption on the design matrix. In addition, we show that this error bound is nearly optimal amongst all differentially private algorithms.

Monday December 7, 2015 19:00 - 23:59

210 C #97

210 C #97

On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of the SGLD with a 1st-order Euler integrator have recently been studied, corresponding theory for general SG-MCMCs has not been explored. In this paper we consider general SG-MCMCs with high-order integrators, and develop theory to analyze finite-time convergence properties and their asymptotic invariant measures. Our theoretical results show faster convergence rates and more accurate invariant measures for SG-MCMCs with higher-order integrators. For example, with the proposed efficient 2nd-order symmetric splitting integrator, the mean square error (MSE) of the posterior average for the SGHMC achieves an optimal convergence rate of $L^{-4/5}$ at $L$ iterations, compared to $L^{-2/3}$ for the SGHMC and SGLD with 1st-order Euler integrators. Furthermore, convergence results of decreasing-step-size SG-MCMCs are also developed, with the same convergence rates as their fixed-step-size counterparts for a specific decreasing sequence. Experiments on both synthetic and real datasets verify our theory, and show advantages of the proposed method in two large-scale real applications.

Monday December 7, 2015 19:00 - 23:59

210 C #64

210 C #64

On the Limitation of Spectral Methods: From the Gaussian Hidden Clique Problem to Rank-One Perturbations of Gaussian Tensors

We consider the following detection problem: given a realization of asymmetric matrix $X$ of dimension $n$, distinguish between the hypothesisthat all upper triangular variables are i.i.d. Gaussians variableswith mean 0 and variance $1$ and the hypothesis that there is aplanted principal submatrix $B$ of dimension $L$ for which all upper triangularvariables are i.i.d. Gaussians with mean $1$ and variance $1$, whereasall other upper triangular elements of $X$ not in $B$ are i.i.d.Gaussians variables with mean 0 and variance $1$. We refer to this asthe `Gaussian hidden clique problem'. When $L=( 1 + \epsilon) \sqrt{n}$ ($\epsilon > 0$), it is possible to solve thisdetection problem with probability $1 - o_n(1)$ by computing thespectrum of $X$ and considering the largest eigenvalue of $X$.We prove that when$L < (1-\epsilon)\sqrt{n}$ no algorithm that examines only theeigenvalues of $X$can detect the existence of a hiddenGaussian clique, with error probability vanishing as $n \to \infty$.The result above is an immediate consequence of a more general result on rank-oneperturbations of $k$-dimensional Gaussian tensors.In this context we establish a lower bound on the criticalsignal-to-noise ratio below which a rank-one signal cannot be detected.

Monday December 7, 2015 19:00 - 23:59

210 C #87

210 C #87

Online Gradient Boosting

We extend the theory of boosting for regression problems to the online learning setting. Generalizing from the batch setting for boosting, the notion of a weak learning algorithm is modeled as an online learning algorithm with linear loss functions that competes with a base class of regression functions, while a strong learning algorithm is an online learning algorithm with smooth convex loss functions that competes with a larger class of regression functions. Our main result is an online gradient boosting algorithm which converts a weak online learning algorithm into a strong one where the larger class of functions is the linear span of the base class. We also give a simpler boosting algorithm that converts a weak online learning algorithm into a strong one where the larger class of functions is the convex hull of the base class, and prove its optimality.

Monday December 7, 2015 19:00 - 23:59

210 C #93

210 C #93

Online Prediction at the Limit of Zero Temperature

We design an online algorithm to classify the vertices of a graph. Underpinning the algorithm is the probability distribution of an Ising model isomorphic to the graph. Each classification is based on predicting the label with maximum marginal probability in the limit of zero-temperature with respect to the labels and vertices seen so far. Computing these classifications is unfortunately based on a $\#P$-complete problem. This motivates us to develop an algorithm for which we give a sequential guarantee in the online mistake bound framework. Our algorithm is optimal when the graph is a tree matching the prior results in [1].For a general graph, the algorithm exploits the additional connectivity over a tree to provide a per-cluster bound. The algorithm is efficient as the cumulative time to sequentially predict all of the vertices of the graph is quadratic in the size of the graph.

Monday December 7, 2015 19:00 - 23:59

210 C #58

210 C #58

Parallel Multi-Dimensional LSTM, With Application to Fast Biomedical Volumetric Image Segmentation

Convolutional Neural Networks (CNNs) can be shifted across 2D images or 3D videos to segment them. They have a fixed input size and typically perceive only small local contexts of the pixels to be classified as foreground or background. In contrast, Multi-Dimensional Recurrent NNs (MD-RNNs) can perceive the entire spatio-temporal context of each pixel in a few sweeps through all pixels, especially when the RNN is a Long Short-Term Memory (LSTM). Despite these theoretical advantages, however, unlike CNNs, previous MD-LSTM variants were hard to parallelise on GPUs. Here we re-arrange the traditional cuboid order of computations in MD-LSTM in pyramidal fashion. The resulting PyraMiD-LSTM is easy to parallelise, especially for 3D data such as stacks of brain slice images. PyraMiD-LSTM achieved best known pixel-wise brain image segmentation results on MRBrainS13 (and competitive results on EM-ISBI12).

Monday December 7, 2015 19:00 - 23:59

210 C #10

210 C #10

Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metric

We consider in this work the space of probability measures $P(X)$ on a Hilbert space $X$ endowed with the 2-Wasserstein metric. Given a finite family of probability measures in $P(X)$, we propose an iterative approach to compute geodesic principal components that summarize efficiently that dataset. The 2-Wasserstein metric provides $P(X)$ with a Riemannian structure and associated concepts (Fr\'echet mean, geodesics, tangent vectors) which prove crucial to follow the intuitive approach laid out by standard principal component analysis. To make our approach feasible, we propose to use an alternative parameterization of geodesics proposed by \citet[\S 9.2]{ambrosio2006gradient}. These \textit{generalized} geodesics are parameterized with two velocity fields defined on the support of the Wasserstein mean of the data, each pointing towards an ending point of the generalized geodesic. The resulting optimization problem of finding principal components is solved by adapting a projected gradient descend method. Experiment results show the ability of the computed principal components to capture axes of variability on histograms and probability measures data.

Monday December 7, 2015 19:00 - 23:59

210 C #48

210 C #48

Probabilistic Variational Bounds for Graphical Models

Variational algorithms such as tree-reweighted belief propagation can provide deterministic bounds on the partition function, but are often loose and difficult to use in an ``any-time'' fashion, expending more computation for tighter bounds. On the other hand, Monte Carlo estimators such as importance sampling have excellent any-time behavior, but depend critically on the proposal distribution. We propose a simple Monte Carlo based inference method that augments convex variational bounds by adding importance sampling (IS). We argue that convex variational methods naturally provide good IS proposals that ``cover" the probability of the target distribution, and reinterpret the variational optimization as designing a proposal to minimizes an upper bound on the variance of our IS estimator. This both provides an accurate estimator and enables the construction of any-time probabilistic bounds that improve quickly and directly on state of-the-art variational bounds, which provide certificates of accuracy given enough samples relative to the error in the initial bound.

Monday December 7, 2015 19:00 - 23:59

210 C #63

210 C #63

Rate-Agnostic (Causal) Structure Learning

Causal structure learning from time series data is a major scientific challenge. Existing algorithms assume that measurements occur sufficiently quickly; more precisely, they assume that the system and measurement timescales are approximately equal. In many scientific domains, however, measurements occur at a significantly slower rate than the underlying system changes. Moreover, the size of the mismatch between timescales is often unknown. This paper provides three distinct causal structure learning algorithms, all of which discover all dynamic graphs that could explain the observed measurement data as arising from undersampling at some rate. That is, these algorithms all learn causal structure without assuming any particular relation between the measurement and system timescales; they are thus "rate-agnostic." We apply these algorithms to data from simulations. The results provide insight into the challenge of undersampling.

Monday December 7, 2015 19:00 - 23:59

210 C #57

210 C #57

Recognizing retinal ganglion cells in the dark

Many neural circuits are composed of numerous distinct cell types that perform different operations on their inputs, and send their outputs to distinct targets. Therefore, a key step in understanding neural systems is to reliably distinguish cell types. An important example is the retina, for which present-day techniques for identifying cell types are accurate, but very labor-intensive. Here, we develop automated classifiers for functional identification of retinal ganglion cells, the output neurons of the retina, based solely on recorded voltage patterns on a large scale array. We use per-cell classifiers based on features extracted from electrophysiological images (spatiotemporal voltage waveforms) and interspike intervals (autocorrelations). These classifiers achieve high performance in distinguishing between the major ganglion cell classes of the primate retina, but fail in achieving the same accuracy in predicting cell polarities (ON vs. OFF). We then show how to use indicators of functional coupling within populations of ganglion cells (cross-correlation) to infer cell polarities with a matrix completion algorithm. This can result in accurate, fully automated methods for cell type classification.

Monday December 7, 2015 19:00 - 23:59

210 C #20

210 C #20

Recursive Training of 2D-3D Convolutional Networks for Neuronal Boundary Prediction

Efforts to automate the reconstruction of neural circuits from 3D electron microscopic (EM) brain images are critical for the field of connectomics. An important computation for reconstruction is the detection of neuronal boundaries. Images acquired by serial section EM, a leading 3D EM technique, are highly anisotropic, with inferior quality along the third dimension. For such images, the 2D max-pooling convolutional network has set the standard for performance at boundary detection. Here we achieve a substantial gain in accuracy through three innovations. Following the trend towards deeper networks for object recognition, we use a much deeper network than previously employed for boundary detection. Second, we incorporate 3D as well as 2D filters, to enable computations that use 3D context. Finally, we adopt a recursively trained architecture in which a first network generates a preliminary boundary map that is provided as input along with the original image to a second network that generates a final boundary map. Backpropagation training is accelerated by ZNN, a new implementation of 3D convolutional networks that uses multicore CPU parallelism for speed. Our hybrid 2D-3D architecture could be more generally applicable to other types of anisotropic 3D images, including video, and our recursive framework for any image labeling problem.

Monday December 7, 2015 19:00 - 23:59

210 C #4

210 C #4

Regressive Virtual Metric Learning

We are interested in supervised metric learning of Mahalanobis like distances. Existing approaches mainly focus on learning a new distance using similarity and dissimilarity constraints between examples. In this paper, instead of bringing closer examples of the same class and pushing far away examples of different classes we propose to move the examples with respect to virtual points. Hence, each example is brought closer to a a priori defined virtual point reducing the number of constraints to satisfy. We show that our approach admits a closed form solution which can be kernelized. We provide a theoretical analysis showing the consistency of the approach and establishing some links with other classical metric learning methods. Furthermore we propose an efficient solution to the difficult problem of selecting virtual points based in part on recent works in optimal transport. Lastly, we evaluate our approach on several state of the art datasets.

Monday December 7, 2015 19:00 - 23:59

210 C #55

210 C #55

Regularization-Free Estimation in Trace Regression with Symmetric Positive Semidefinite Matrices

Trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoyed great popularity. In this paper, we argue that such regularization may no longer be necessary if the underlying matrix is symmetric positive semidefinite (spd) and the design satisfies certain conditions. In this situation, simple least squares estimation subject to an spd constraint may perform as well as regularization-based approaches with a proper choice of regularization parameter, which entails knowledge of the noise level and/or tuning. By contrast, constrained least squaresestimation comes without any tuning parameter and may hence be preferred due to its simplicity.

Monday December 7, 2015 19:00 - 23:59

210 C #94

210 C #94

Regularized EM Algorithms: A Unified Framework and Statistical Guarantees

Latent models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet our rigorous understanding of its performance is highly incomplete. Recently, work in [1] has demonstrated that for an important class of problems, EM exhibits linear local convergence. In the high-dimensional setting, however, the M-step may not be well defined. We address precisely this setting through a unified treatment using regularization. While regularization for high-dimensional problems is by now well understood, the iterative EM algorithm requires a careful balancing of making progress towards the solution while identifying the right structure (e.g., sparsity or low-rank). In particular, regularizing the M-step using the state-of-the-art high-dimensional prescriptions (e.g., \`a la [19]) is not guaranteed to provide this balance. Our algorithm and analysis are linked in a way that reveals the balance between optimization and statistical errors. We specialize our general framework to sparse gaussian mixture models, high-dimensional mixed regression, and regression with missing variables, obtaining statistical guarantees for each of these examples.

Monday December 7, 2015 19:00 - 23:59

210 C #88

210 C #88

Rethinking LDA: Moment Matching for Discrete ICA

We consider moment matching techniques for estimation in Latent Dirichlet Allocation (LDA). By drawing explicit links between LDA and discrete versions of independent component analysis (ICA), we first derive a new set of cumulant-based tensors, with an improved sample complexity. Moreover, we reuse standard ICA techniques such as joint diagonalization of tensors to improve over existing methods based on the tensor power method. In an extensive set of experiments on both synthetic and real datasets, we show that our new combination of tensors and orthogonal joint diagonalization techniques outperforms existing moment matching methods.

Monday December 7, 2015 19:00 - 23:59

210 C #39

210 C #39

Robust Feature-Sample Linear Discriminant Analysis for Brain Disorders Diagnosis

A wide spectrum of discriminative methods is increasingly used in diverse applications for classification or regression tasks. However, many existing discriminative methods assume that the input data is nearly noise-free, which limits their applications to solve real-world problems. Particularly for disease diagnosis, the data acquired by the neuroimaging devices are always prone to different sources of noise. Robust discriminative models are somewhat scarce and only a few attempts have been made to make them robust against noise or outliers. These methods focus on detecting either the sample-outliers or feature-noises. Moreover, they usually use unsupervised de-noising procedures, or separately de-noise the training and the testing data. All these factors may induce biases in the learning process, and thus limit its performance. In this paper, we propose a classification method based on the least-squares formulation of linear discriminant analysis, which simultaneously detects the sample-outliers and feature-noises. The proposed method operates under a semi-supervised setting, in which both labeled training and unlabeled testing data are incorporated to form the intrinsic geometry of the sample space. Therefore, the violating samples or feature values are identified as sample-outliers or feature-noises, respectively. We test our algorithm on one synthetic and two brain neurodegenerative databases (particularly for Parkinson's disease and Alzheimer's disease). The results demonstrate that our method outperforms all baseline and state-of-the-art methods, in terms of both accuracy and the area under the ROC curve.

Monday December 7, 2015 19:00 - 23:59

210 C #30

210 C #30

Robust Gaussian Graphical Modeling with the Trimmed Graphical Lasso

Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Trimmed Graphical Lasso for robust estimation of sparse GGMs. Our method guards against outliers by an implicit trimming mechanism akin to the popular Least Trimmed Squares method used for linear regression. We provide a rigorous statistical analysis of our estimator in the high-dimensional setting. In contrast, existing approaches for robust sparse GGMs estimation lack statistical guarantees. Our theoretical results are complemented by experiments on simulated and real gene expression data which further demonstrate the value of our approach.

Monday December 7, 2015 19:00 - 23:59

210 C #71

210 C #71

Robust PCA with compressed data

The robust principal component analysis (RPCA) problem seeks to separate low-rank trends from sparse outlierswithin a data matrix, that is, to approximate a $n\times d$ matrix $D$ as the sum of a low-rank matrix $L$ and a sparse matrix $S$.We examine the robust principal component analysis (RPCA) problem under data compression, wherethe data $Y$ is approximately given by $(L + S)\cdot C$, that is, a low-rank $+$ sparse data matrix that has been compressed to size $n\times m$ (with $m$ substantially smaller than the original dimension $d$) via multiplication witha compression matrix $C$. We give a convex program for recovering the sparse component $S$ along with the compressed low-rank component $L\cdot C$, along with upper bounds on the error of this reconstructionthat scales naturally with the compression dimension $m$ and coincides with existing results for the uncompressedsetting $m=d$. Our results can also handle error introduced through additive noise or through missing data.The scaling of dimension, compression, and signal complexity in our theoretical results is verified empirically through simulations, and we also apply our method to a data set measuring chlorine concentration acrossa network of sensors, to test its performance in practice.

Monday December 7, 2015 19:00 - 23:59

210 C #73

210 C #73

Robust Portfolio Optimization

We propose a robust portfolio optimization approach based on quantile statistics. The proposed method is robust to extreme events in asset returns, and accommodates large portfolios under limited historical data. Specifically, we show that the risk of the estimated portfolio converges to the oracle optimal risk with parametric rate under weakly dependent asset returns. The theory does not rely on higher order moment assumptions, thus allowing for heavy-tailed asset returns. Moreover, the rate of convergence quantifies that the size of the portfolio under management is allowed to scale exponentially with the sample size of the historical data. The empirical effectiveness of the proposed method is demonstrated under both synthetic and real stock data. Our work extends existing ones by achieving robustness in high dimensions, and by allowing serial dependence.

Monday December 7, 2015 19:00 - 23:59

210 C #82

210 C #82

Sample Complexity Bounds for Iterative Stochastic Policy Optimization

This paper is concerned with robustness analysis of decision making under uncertainty. We consider a class of iterative stochastic policy optimization problems and analyze the resulting expected performance for each newly updated policy at each iteration. In particular, we employ concentration-of-measure inequalities to compute future expected cost and probability of constraint violation using empirical runs. A novel inequality bound is derived that accounts for the possibly unbounded change-of-measure likelihood ratio resulting from iterative policy adaptation. The bound serves as a high-confidence certificate for providing future performance or safety guarantees. The approach is illustrated with a simple robot control scenario and initial steps towards applications to challenging aerial vehicle navigation problems are presented.

Monday December 7, 2015 19:00 - 23:59

210 C #61

210 C #61

Scalable Adaptation of State Complexity for Nonparametric Hidden Markov Models

Bayesian nonparametric hidden Markov models are typically learned via fixed truncations of the infinite state space or local Monte Carlo proposals that make small changes to the state space. We develop an inference algorithm for the sticky hierarchical Dirichlet process hidden Markov model that scales to big datasets by processing a few sequences at a time yet allows rapid adaptation of the state space cardinality. Unlike previous point-estimate methods, our novel variational bound penalizes redundant or irrelevant states and thus enables optimization of the state space. Our birth proposals use observed data statistics to create useful new states that escape local optima. Merge and delete proposals remove ineffective states to yield simpler models with more affordable future computations. Experiments on speaker diarization, motion capture, and epigenetic chromatin datasets discover models that are more compact, more interpretable, and better aligned to ground truth segmentations than competitors. We have released an open-source Python implementation which can parallelize local inference steps across sequences.

Monday December 7, 2015 19:00 - 23:59

210 C #29

210 C #29

Scalable Inference for Gaussian Process Models with Black-Box Likelihoods

We propose a sparse method for scalable automated variational inference (AVI) in a large class of models with Gaussian process (GP) priors, multiple latent functions, multiple outputs and non-linear likelihoods. Our approach maintains the statistical efficiency property of the original AVI method, requiring only expectations over univariate Gaussian distributions to approximate the posterior with a mixture of Gaussians. Experiments on small datasets for various problems including regression, classification, Log Gaussian Cox processes, and warped GPs show that our method can perform as well as the full method under high levels of sparsity. On larger experiments using the MNIST and the SARCOS datasets we show that our method can provide superior performance to previously published scalable approaches that have been handcrafted to specific likelihood models.

Monday December 7, 2015 19:00 - 23:59

210 C #33

210 C #33

Semi-Supervised Factored Logistic Regression for High-Dimensional Neuroimaging Data

Imaging neuroscience links human behavior to aspects of brain biology in ever-increasing datasets. Existing neuroimaging methods typically perform either discovery of unknown neural structure or testing of neural structure associated with mental tasks. However, testing hypotheses on the neural correlates underlying larger sets of mental tasks necessitates adequate representations for the observations. We therefore propose to blend representation modelling and task classification into a unified statistical learning problem. A multinomial logistic regression is introduced that is constrained by factored coefficients and coupled with an autoencoder. We show that this approach yields more accurate and interpretable neural models of psychological tasks in a reference dataset, as well as better generalization to other datasets.

Monday December 7, 2015 19:00 - 23:59

210 C #14

210 C #14

Smooth and Strong: MAP Inference with Linear Convergence

Maximum a-posteriori (MAP) inference is an important task for many applications. Although the standard formulation gives rise to a hard combinatorial optimization problem, several effective approximations have been proposed and studied in recent years. We focus on linear programming (LP) relaxations, which have achieved state-of-the-art performance in many applications. However, optimization of the resulting program is in general challenging due to non-smoothness and complex non-separable constraints.Therefore, in this work we study the benefits of augmenting the objective function of the relaxation with strong convexity. Specifically, we introduce strong convexity by adding a quadratic term to the LP relaxation objective. We provide theoretical guarantees for the resulting programs, bounding the difference between their optimal value and the original optimum. Further, we propose suitable optimization algorithms and analyze their convergence.

Monday December 7, 2015 19:00 - 23:59

210 C #78

210 C #78

Spectral Norm Regularization of Orthonormal Representations for Graph Transduction

**Speakers**
## Prof Chiranjib Bhattacharyya

Recent literature~\cite{ando} suggests that embedding a graph on an unit sphere leads to better generalization for graph transduction. However, the choice of optimal embedding and an efficient algorithm to compute the same remains open. In this paper, we show that orthonormal representations, a class of unit-sphere graph embeddings are PAC learnable. Existing PAC-based analysis do not apply as the VC dimension of the function class is infinite. We propose an alternative PAC-based bound, which do not depend on the VC dimension of the underlying function class, but is related to the famous Lov\'{a}sz~$\vartheta$ function. The main contribution of the paper is SPORE, a SPectral regularized ORthonormal Embedding for graph transduction, derived from the PAC bound. SPORE is posed as a non-smooth convex function over an \emph{elliptope}. These problems are usually solved as semi-definite programs (SDPs) with time complexity $O(n^6)$. We present, Infeasible Inexact proximal~(IIP): an Inexact proximal method which performs subgradient procedure on an approximate projection, not necessarily feasible. IIP is more scalable than SDP, has an $O(\frac{1}{\sqrt{T}})$ convergence, and is generally applicable whenever a suitable approximate projection is available. We use IIP to compute SPORE where the approximate projection step is computed by FISTA, an accelerated gradient descent procedure. We show that the method has a convergence rate of $O(\frac{1}{\sqrt{T}})$. The proposed algorithm easily scales to 1000's of vertices, while the standard SDP computation does not scale beyond few hundred vertices. Furthermore, the analysis presented here easily extends to the multiple graph setting.

Professor Dept of Comp. Science & Automation, Indian Institute of Science - Bangalore

Chiranjib Bhattacharyya is currently Professor in the Department of Computer Science and Automation, Indian Institute of Science. His research interests are in Machine Learning, Optimisation and their applications to Industrial problems. He joined the Department of CSA, IISc, in 2002 as an Assistant Professor. Prior to joining the Department he was a postdoctoral fellow at UC Berkeley. He holds BE and ME degrees, both in Electrical... Read More →

Monday December 7, 2015 19:00 - 23:59

210 C #80

210 C #80

Spectral Representations for Convolutional Neural Networks

Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs).We employ spectral representations to introduce a number of innovations to CNN design. First, we propose spectral pooling, which performs dimensionality reduction by truncating the representation in the frequency domain. This approach preserves considerably more information per parameter than other pooling strategies and enables flexibility in the choice of pooling output dimensionality. This representation also enables a new form of stochastic regularization by randomized modification of resolution. We show that these methods achieve competitive results on classification and approximation tasks, without using any dropout or max-pooling. Finally, we demonstrate the effectiveness of complex-coefficient spectral parameterization of convolutional filters. While this leaves the underlying model unchanged, it results in a representation that greatly facilitates optimization. We observe on a variety of popular CNN configurations that this leads to significantly faster convergence during training.

Monday December 7, 2015 19:00 - 23:59

210 C #17

210 C #17

Statistical Model Criticism using Kernel Two Sample Tests

We propose an exploratory approach to statistical model criticism using maximum mean discrepancy (MMD) two sample tests. Typical approaches to model criticism require a practitioner to select a statistic by which to measure discrepancies between data and a statistical model. MMD two sample tests are instead constructed as an analytic maximisation over a large space of possible statistics and therefore automatically select the statistic which most shows any discrepancy. We demonstrate on synthetic data that the selected statistic, called the witness function, can be used to identify where a statistical model most misrepresents the data it was trained on. We then apply the procedure to real data where the models being assessed are restricted Boltzmann machines, deep belief networks and Gaussian process regression and demonstrate the ways in which these models fail to capture the properties of the data they are trained on.

Monday December 7, 2015 19:00 - 23:59

210 C #25

210 C #25

StopWasting My Gradients: Practical SVRG

We present and analyze several strategies for improving the performance ofstochastic variance-reduced gradient (SVRG) methods. We first show that theconvergence rate of these methods can be preserved under a decreasing sequenceof errors in the control variate, and use this to derive variants of SVRG that usegrowing-batch strategies to reduce the number of gradient calculations requiredin the early iterations. We further (i) show how to exploit support vectors to reducethe number of gradient computations in the later iterations, (ii) prove that thecommonly–used regularized SVRG iteration is justified and improves the convergencerate, (iii) consider alternate mini-batch selection strategies, and (iv) considerthe generalization error of the method.

Monday December 7, 2015 19:00 - 23:59

210 C #79

210 C #79

Subspace Clustering with Irrelevant Features via Robust Dantzig Selector

This paper considers the subspace clustering problem where the data contains irrelevant or corrupted features. We propose a method termed ``robust Dantzig selector'' which can successfully identify the clustering structure even with the presence of irrelevant features. The idea is simple yet powerful: we replace the inner product by its robust counterpart, which is insensitive to the irrelevant features given an upper bound of the number of irrelevant features. We establish theoretical guarantees for the algorithm to identify the correct subspace, and demonstrate the effectiveness of the algorithm via numerical simulations. To the best of our knowledge, this is the first method developed to tackle subspace clustering with irrelevant features.

Monday December 7, 2015 19:00 - 23:59

210 C #75

210 C #75

Sum-of-Squares Lower Bounds for Sparse PCA

This paper establishes a statistical versus computational trade-offfor solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis} (Sparse PCA) problem, and the family of {\em Sum-of-Squares} (SoS, aka Lasserre/Parillo) convex relaxations. It was well known that in large dimension $p$, a planted $k$-sparse unit vector can be {\em in principle} detected using only $n \approx k\log p$ (Gaussian or Bernoulli) samples, but all {\em efficient} (polynomial time) algorithms known require $n \approx k^2 $ samples. It was also known that this quadratic gap cannot be improved by the the most basic {\em semi-definite} (SDP, aka spectral) relaxation, equivalent to a degree-2 SoS algorithms. Here we prove that also degree-4 SoS algorithms cannot improve this quadratic gap. This average-case lower bound adds to the small collection of hardness results in machine learning for this powerful family of convex relaxation algorithms. Moreover, our design of moments (or ``pseudo-expectations'') for this lower bound is quite different than previous lower bounds. Establishing lower bounds for higher degree SoS algorithms for remains a challenging problem.

Monday December 7, 2015 19:00 - 23:59

210 C #92

210 C #92

Supervised Learning for Dynamical System Learning

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoffbetween computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporateprior information such as sparsity or structure. To address this problem, we presenta new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, therebyallowing users to incorporate prior knowledge via standard techniques such asL 1 regularization. Many existing spectral methods are special cases of this newframework, using linear regression as the supervised learner. We demonstrate theeffectiveness of our framework by showing examples where nonlinear regressionor lasso let us learn better state representations than plain linear regression does;the correctness of these instances follows directly from our general analysis.

Monday December 7, 2015 19:00 - 23:59

210 C #41

210 C #41

Taming the Wild: A Unified Analysis of Hogwild-Style Algorithms

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and reduced precision. Our main result is a martingale-based analysis that enables us to capture the rich noise models that may arise from such techniques. Specifically, we useour new analysis in three ways: (1) we derive convergence rates for the convex case (Hogwild) with relaxed assumptions on the sparsity of the problem; (2) we analyze asynchronous SGD algorithms for non-convex matrix problems including matrix completion; and (3) we design and analyze an asynchronous SGD algorithm, called Buckwild, that uses lower-precision arithmetic. We show experimentally that our algorithms run efficiently for a variety of problems on modern hardware.

Monday December 7, 2015 19:00 - 23:59

210 C #85

210 C #85

Texture Synthesis Using Convolutional Neural Networks

Here we introduce a new model of natural textures based on the feature spaces of convolutional neural networks optimised for object recognition. Samples from the model are of high perceptual quality demonstrating the generative power of neural networks trained in a purely discriminative fashion. Within the model, textures are represented by the correlations between feature maps in several layers of the network. We show that across layers the texture representations increasingly capture the statistical properties of natural images while making object information more and more explicit. The model provides a new tool to generate stimuli for neuroscience and might offer insights into the deep representations learned by convolutional neural networks.

Monday December 7, 2015 19:00 - 23:59

210 C #1

210 C #1

The Poisson Gamma Belief Network

To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upward-downward Gibbs sampler, each iteration of which upward samples Dirichlet distributed connection weight vectors starting from the first layer (bottom data layer), and then downward samples gamma distributed hidden units starting from the top hidden layer. The gamma-negative binomial process combined with a layer-wise training strategy allows the PGBN to infer the width of each layer given a fixed budget on the width of the first layer. The PGBN with a single hidden layer reduces to Poisson factor analysis. Example results on text analysis illustrate interesting relationships between the width of the first layer and the inferred network structure, and demonstrate that the PGBN, whose hidden units are imposed with correlated gamma priors, can add more layers to increase its performance gains over Poisson factor analysis, given the same limit on the width of the first layer.

Monday December 7, 2015 19:00 - 23:59

210 C #13

210 C #13

Tractable Learning for Complex Probability Queries

Tractable learning aims to learn probabilistic models where inference is guaranteed to be efficient. However, the particular class of queries that is tractable depends on the model and underlying representation. Usually this class is MPE or conditional probabilities $\Pr(\xs|\ys)$ for joint assignments~$\xs,\ys$. We propose a tractable learner that guarantees efficient inference for a broader class of queries. It simultaneously learns a Markov network and its tractable circuit representation, in order to guarantee and measure tractability. Our approach differs from earlier work by using Sentential Decision Diagrams (SDD) as the tractable language instead of Arithmetic Circuits (AC). SDDs have desirable properties, which more general representations such as ACs lack, that enable basic primitives for Boolean circuit compilation. This allows us to support a broader class of complex probability queries, including counting, threshold, and parity, in polytime.

Monday December 7, 2015 19:00 - 23:59

210 C #44

210 C #44

Variational Dropout and the Local Reparameterization Trick

We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant w.r.t. the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence.We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose \emph{variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.

Monday December 7, 2015 19:00 - 23:59

210 C #34

210 C #34

Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning

The mutual information is a core statistical quantity that has applications in all areas of machine learning, whether this is in training of density models over multiple data modalities, in maximising the efficiency of noisy transmission channels, or when learning behaviour policies for exploration by artificial agents. Most learning algorithms that involve optimisation of the mutual information rely on the Blahut-Arimoto algorithm --- an enumerative algorithm with exponential complexity that is not suitable for modern machine learning applications. This paper provides a new approach for scalable optimisation of the mutual information by merging techniques from variational inference and deep learning. We develop our approach by focusing on the problem of intrinsically-motivated learning, where the mutual information forms the definition of a well-known internal drive known as empowerment. Using a variational lower bound on the mutual information, combined with convolutional networks for handling visual input streams, we develop a stochastic optimisation algorithm that allows for scalable information maximisation and empowerment-based reasoning directly from pixels to actions.

Monday December 7, 2015 19:00 - 23:59

210 C #36

210 C #36

Weakly-supervised Disentangling with Recurrent Transformations for 3D View Synthesis

An important problem for both graphics and vision is to synthesize novel views of a 3D object from a single image. This is in particular challenging due to the partial observability inherent in projecting a 3D object onto the image space, and the ill-posedness of inferring object shape and pose. However, we can train a neural network to address the problem if we restrict our attention to specific object classes (in our case faces and chairs) for which we can gather ample training data. In this paper, we propose a novel recurrent convolutional encoder-decoder network that is trained end-to-end on the task of rendering rotated objects starting from a single image. The recurrent structure allows our model to capture long- term dependencies along a sequence of transformations, and we demonstrate the quality of its predictions for human faces on the Multi-PIE dataset and for a dataset of 3D chair models, and also show its ability of disentangling latent data factors without using object class labels.

Monday December 7, 2015 19:00 - 23:59

210 C #7

210 C #7

Beyond Convexity: Stochastic Quasi-Convex Optimization

This poster has been moved from Monday #86 to Thursday #101.

Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD).The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves. In this paper we analyze a stochastic version of NGD and prove its convergence to a global minimum for a wider class of functions: we require the functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens the concept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient descent. Locally-Lipschitz functions are only required to be Lipschitz in a small region around the optimum. This assumption circumvents gradient explosion, which is another known hurdle for gradient descent variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size.

Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD).The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves. In this paper we analyze a stochastic version of NGD and prove its convergence to a global minimum for a wider class of functions: we require the functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens the concept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient descent. Locally-Lipschitz functions are only required to be Lipschitz in a small region around the optimum. This assumption circumvents gradient explosion, which is another known hurdle for gradient descent variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size.

Monday December 7, 2015 19:00 - Saturday December 12, 2015 18:00

210 C #86

210 C #86

Probabilistic Machine Learning: Foundations and Frontiers

Probabilistic modelling provides a mathematical framework for understanding what learning is, and has therefore emerged as one of the principal approaches for designing computer algorithms that learn from data acquired through experience. I will review the foundations of this field, from basics to Bayesian nonparametric models and scalable inference. I will then highlight some current areas of research at the frontiers of machine learning, leading up to topics such as probabilistic programming, Bayesian optimisation, the rational allocation of computational resources, and the Automatic Statistician.

Tuesday December 8, 2015 09:00 - 09:50

Room 210 AB

Room 210 AB

Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition

Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate than simpler sketching algorithms, yet still converges quickly for *any* matrix, independently of singular value gaps. After ~O(1/epsilon) iterations, it gives a low-rank approximation within (1+epsilon) of optimal for spectral norm error.We give the first provable runtime improvement on Simultaneous Iteration: a randomized block Krylov method, closely related to the classic Block Lanczos algorithm, gives the same guarantees in just ~O(1/sqrt(epsilon)) iterations and performs substantially better experimentally. Our analysis is the first of a Krylov subspace method that does not depend on singular value gaps, which are unreliable in practice.Furthermore, while it is a simple accuracy benchmark, even (1+epsilon) error for spectral norm low-rank approximation does not imply that an algorithm returns high quality principal components, a major issue for data applications. We address this problem for the first time by showing that both Block Krylov Iteration and Simultaneous Iteration give nearly optimal PCA for any matrix. This result further justifies their strength over non-iterative sketching methods.

Tuesday December 8, 2015 09:50 - 10:10

Room 210 A

Room 210 A

b-bit Marginal Regression

We consider the problem of sparse signal recovery from $m$ linear measurements quantized to $b$ bits. $b$-bit Marginal Regression is proposed as recovery algorithm. We study the question of choosing $b$ in the setting of a given budget of bits $B = m \cdot b$ and derive a single easy-to-compute expression characterizing the trade-off between $m$ and $b$. The choice $b = 1$ turns out to be optimal for estimating the unit vector corresponding to the signal for any level of additive Gaussian noise before quantization as well as for adversarial noise. For $b \geq 2$, we show that Lloyd-Max quantization constitutes an optimal quantization scheme and that the norm of the signal canbe estimated consistently by maximum likelihood.

Tuesday December 8, 2015 10:10 - 10:35

Room 210 A

Room 210 A

LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements

Consider estimating an unknown, but structured (e.g. sparse, low-rank, etc.), signal $x_0\in R^n$ from a vector $y\in R^m$ of measurements of the form $y_i=g_i(a_i^Tx_0)$, where the $a_i$'s are the rows of a known measurement matrix $A$, and, $g$ is a (potentially unknown) nonlinear and random link-function. Such measurement functions could arise in applications where the measurement device has nonlinearities and uncertainties. It could also arise by design, e.g., $g_i(x)=sign(x+z_i)$, corresponds to noisy 1-bit quantized measurements. Motivated by the classical work of Brillinger, and more recent work of Plan and Vershynin, we estimate $x_0$ via solving the Generalized-LASSO, i.e., $\hat x=\arg\min_{x}\|y-Ax_0\|_2+\lambda f(x)$ for some regularization parameter $\lambda >0$ and some (typically non-smooth) convex regularizer $f$ that promotes the structure of $x_0$, e.g. $\ell_1$-norm, nuclear-norm. While this approach seems to naively ignore the nonlinear function $g$, both Brillinger and Plan and Vershynin have shown that, when the entries of $A$ are iid standard normal, this is a good estimator of $x_0$ up to a constant of proportionality $\mu$, which only depends on $g$. In this work, we considerably strengthen these results by obtaining explicit expressions for $\|\hat x-\mu x_0\|_2$, for the regularized Generalized-LASSO, that are asymptotically precise when $m$ and $n$ grow large. A main result is that the estimation performance of the Generalized LASSO with non-linear measurements is asymptotically the same as one whose measurements are linear $y_i=\mu a_i^Tx_0+\sigma z_i$, with $\mu=E[\gamma g(\gamma)]$ and $\sigma^2=E[(g(\gamma)-\mu\gamma)^2]$, and, $\gamma$ standard normal. The derived expressions on the estimation performance are the first-known precise results in this context. One interesting consequence of our result is that the optimal quantizer of the measurements that minimizes the estimation error of the LASSO is the celebrated Lloyd-Max quantizer.

Tuesday December 8, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Minimum Weight Perfect Matching via Blossom Belief Propagation

Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this paper, we develop the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds' algorithm as a sequence of LPs.

Tuesday December 8, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Optimal Rates for Random Fourier Features

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show good versatility, they are computationally intensive and have poor scalability to large data as they require operations on Gram matrices. In order to mitigate this serious computational limitation, recently randomized constructions have been proposed in the literature, which allow the application of fast linear algorithms. Random Fourier features (RFF) are among the most popular and widely applied constructions: they provide an easily computable, low-dimensional feature representation for shift-invariant kernels. Despite the popularity of RFFs, very little is understood theoretically about their approximation quality. In this paper, we provide a detailed finite-sample theoretical analysis about the approximation quality of RFFs by (i) establishing optimal (in terms of the RFF dimension, and growing set size) performance guarantees in uniform norm, and (ii) presenting guarantees in L^r (1 ≤ r < ∞) norms. We also propose an RFF approximation to derivatives of a kernel with a theoretical study on its approximation quality.

Tuesday December 8, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Submodular Hamming Metrics

We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tractable to optimize over. By exploiting submodularity, we are able to give hardness results and approximation algorithms for optimizing over such metrics. Additionally, we demonstrate empirically the effectiveness of these metrics and associated algorithms on both a metric minimization task (a form of clustering) and also a metric maximization task (generating diverse k-best lists).

Tuesday December 8, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Super-Resolution Off the Grid

Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to biology to spectroscopy, where it is common to take (coarse) Fourier measurements of an object. Of particular interest is in obtaining estimation procedures which are robust to noise, with the following desirable statistical and computational properties: we seek to use coarse Fourier measurements (bounded by some \emph{cutoff frequency}); we hope to take a (quantifiably) small number of measurements; we desire our algorithm to run quickly. Suppose we have $k$ point sources in $d$ dimensions, where the points are separated by at least $\Delta$ from each other (in Euclidean distance). This work provides an algorithm with the following favorable guarantees:1. The algorithm uses Fourier measurements, whose frequencies are bounded by $O(1/\Delta)$ (up to log factors). Previous algorithms require a \emph{cutoff frequency} which may be as large as $\Omega(\sqrt{d}/\Delta)$.2. The number of measurements taken by and the computational complexity of our algorithm are bounded by a polynomial in both the number of points $k$ and the dimension $d$, with \emph{no} dependence on the separation $\Delta$. In contrast, previous algorithms depended inverse polynomially on the minimal separation and exponentially on the dimension for both of these quantities.Our estimation procedure itself is simple: we take random bandlimited measurements (as opposed to taking an exponential number of measurements on the hyper-grid). Furthermore, our analysis and algorithm are elementary (based on concentration bounds of sampling and singular value decomposition).

Tuesday December 8, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Top-k Multiclass SVM

Class ambiguity is typical in image classification problems with a large number of classes. When classes are difficult to discriminate, it makes sense to allow k guesses and evaluate classifiers based on the top-k error instead of the standard zero-one loss. We propose top-k multiclass SVM as a direct method to optimize for top-k performance. Our generalization of the well-known multiclass SVM is based on a tight convex upper bound of the top-k error. We propose a fast optimization scheme based on an efficient projection onto the top-k simplex, which is of its own interest. Experiments on five datasets show consistent improvements in top-k accuracy compared to various baselines.

Tuesday December 8, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Sampling from Probabilistic Submodular Models

Submodular and supermodular functions have found wide applicability in machine learning, capturing notions such as diversity and regularity, respectively. These notions have deep consequences for optimization, and the problem of (approximately) optimizing submodular functions has received much attention. However, beyond optimization, these notions allow specifying expressive probabilistic models that can be used to quantify predictive uncertainty via marginal inference. Prominent, well-studied special cases include Ising models and determinantal point processes, but the general class of log-submodular and log-supermodular models is much richer and little studied. In this paper, we investigate the use of Markov chain Monte Carlo sampling to perform approximate inference in general log-submodular and log-supermodular models. In particular, we consider a simple Gibbs sampling procedure, and establish two sufficient conditions, the first guaranteeing polynomial-time, and the second fast (O(nlogn)) mixing. We also evaluate the efficiency of the Gibbs sampler on three examples of such models, and compare against a recently proposed variational approach.

Tuesday December 8, 2015 10:55 - 11:35

Room 210 A

Room 210 A

Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems

This paper is concerned with finding a solution x to a quadratic system of equations y_i = |< a_i, x >|^2, i = 1, 2, ..., m. We prove that it is possible to solve unstructured quadratic systems in n variables exactly from O(n) equations in linear time, that is, in time proportional to reading and evaluating the data. This is accomplished by a novel procedure, which starting from an initial guess given by a spectral initialization procedure, attempts to minimize a non-convex objective. The proposed algorithm distinguishes from prior approaches by regularizing the initialization and descent procedures in an adaptive fashion, which discard terms bearing too much influence on the initial estimate or search directions. These careful selection rules---which effectively serve as a variance reduction scheme---provide a tighter initial guess, more robust descent directions, and thus enhanced practical performance. Further, this procedure also achieves a near-optimal statistical accuracy in the presence of noise. Finally, we demonstrate empirically that the computational cost of our algorithm is about four times that of solving a least-squares problem of the same size.

Tuesday December 8, 2015 10:55 - 11:35

Room 210 A

Room 210 A

Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization

The asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and speedup properties, mainly due to the nonconvexity of most deep learning formulations and the asynchronous parallel mechanism. To fill the gaps in theory and provide theoretical supports, this paper studies two asynchronous parallel implementations of SG: one is on the computer network and the other is on the shared memory system. We establish an ergodic convergence rate $O(1/\sqrt{K})$ for both algorithms and prove that the linear speedup is achievable if the number of workers is bounded by $\sqrt{K}$ ($K$ is the total number of iterations). Our results generalize and improve existing analysis for convex minimization.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Distributed Submodular Cover: Succinctly Summarizing Massive Data

How can one find a subset, ideally as small as possible, that well represents a massive dataset? I.e., its corresponding utility, measured according to a suitable utility function, should be comparable to that of the whole dataset. In this paper, we formalize this challenge as a submodular cover problem. Here, the utility is assumed to exhibit submodularity, a natural diminishing returns condition preva- lent in many data summarization applications. The classical greedy algorithm is known to provide solutions with logarithmic approximation guarantees compared to the optimum solution. However, this sequential, centralized approach is imprac- tical for truly large-scale problems. In this work, we develop the first distributed algorithm – DISCOVER – for submodular set cover that is easily implementable using MapReduce-style computations. We theoretically analyze our approach, and present approximation guarantees for the solutions returned by DISCOVER. We also study a natural trade-off between the communication cost and the num- ber of rounds required to obtain such a solution. In our extensive experiments, we demonstrate the effectiveness of our approach on several applications, includ- ing active set selection, exemplar based clustering, and vertex cover on tens of millions of data points using Spark.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Distributionally Robust Logistic Regression

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this Wasserstein ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high confidence. We then formulate a distributionally robust logistic regression model that minimizes a worst-case expected logloss function, where the worst case is taken over all distributions in the Wasserstein ball. We prove that this optimization problem admits a tractable reformulation and encapsulates the classical as well as the popular regularized logistic regression problems as special cases. We further propose a distributionally robust approach based on Wasserstein balls to compute upper and lower confidence bounds on the misclassification probability of the resulting classifier. These bounds are given by the optimal values of two highly tractable linear programs. We validate our theoretical out-of-sample guarantees through simulated and empirical experiments.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Extending Gossip Algorithms to Distributed Estimation of U-statistics

Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of U-statistics, relying on more expensive averaging over pairs of observations, is a less investigated area. Yet, such data functionals are essential to describe global properties of a statistical population, with important examples including Area Under the Curve, empirical variance, Gini mean difference and within-cluster point scatter. This paper proposes new synchronous and asynchronous randomized gossip algorithms which simultaneously propagate data across the network and maintain local estimates of the U-statistic of interest. We establish convergence rate bounds of O(1 / t) and O(log t / t) for the synchronous and asynchronous cases respectively, where t is the number of iterations, with explicit data and network dependent terms. Beyond favorable comparisons in terms of rate analysis, numerical experiments provide empirical evidence the proposed algorithms surpasses the previously introduced approach.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees

There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. An important challenge is to reconcile these probabilistic integrators with rigorous convergence guarantees. In this paper, we present the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ). Under FWBQ, convergence to the true value of the integral is shown to be exponential and posterior contraction rates are proven to be superexponential. In simulations, FWBQ is competitive with state-of-the-art methods and out-performs alternatives based on Frank-Wolfe optimisation. Our approach is applied to successfully quantify numerical error in the solution to a challenging model choice problem in cellular biology.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Newton-Stein Method: A Second Order Method for GLMs via Stein's Lemma

We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs)when the number of observations is much larger than the number of coefficients (n > > p > > 1). In this regime, optimization algorithms can immensely benefit fromapproximate second order information.We propose an alternative way of constructing the curvature information by formulatingit as an estimation problem and applying a Stein-type lemma, which allows further improvements through sub-sampling andeigenvalue thresholding.Our algorithm enjoys fast convergence rates, resembling that of second order methods, with modest per-iteration cost. We provide its convergence analysis for the case where the rows of the design matrix are i.i.d. samples with bounded support.We show that the convergence has two phases, aquadratic phase followed by a linear phase. Finally,we empirically demonstrate that our algorithm achieves the highest performancecompared to various algorithms on several datasets.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

On some provably correct cases of variational inference for topic models

Variational inference is an efficient, popular heuristic used in the context of latent variable models. We provide the first analysis of instances where variational inference algorithms converge to the global optimum, in the setting of topic models. Our initializations are natural, one of them being used in LDA-c, the mostpopular implementation of variational inference.In addition to providing intuition into why this heuristic might work in practice, the multiplicative, rather than additive nature of the variational inference updates forces us to usenon-standard proof arguments, which we believe might be of general theoretical interest.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

The Self-Normalized Estimator for Counterfactual Learning

This paper identifies a severe problem of the counterfactual risk estimator typically used in batch learning from logged bandit feedback (BLBF), and proposes the use of an alternative estimator that avoids this problem.In the BLBF setting, the learner does not receive full-information feedback like in supervised learning, but observes feedback only for the actions taken by a historical policy.This makes BLBF algorithms particularly attractive for training online systems (e.g., ad placement, web search, recommendation) using their historical logs.The Counterfactual Risk Minimization (CRM) principle offers a general recipe for designing BLBF algorithms. It requires a counterfactual risk estimator, and virtually all existing works on BLBF have focused on a particular unbiased estimator.We show that this conventional estimator suffers from apropensity overfitting problem when used for learning over complex hypothesis spaces.We propose to replace the risk estimator with a self-normalized estimator, showing that it neatly avoids this problem.This naturally gives rise to a new learning algorithm -- Normalized Policy Optimizer for Exponential Models (Norm-POEM) --for structured output prediction using linear rules.We evaluate the empirical effectiveness of Norm-POEM on severalmulti-label classification problems, finding that it consistently outperforms the conventional estimator.

Tuesday December 8, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Incremental Methods for Additive Cost Convex Optimization

Motivated by machine learning problems over large data sets and distributed optimization over networks, we consider the problem of minimizing the sum of a large number of convex component functions. We study incremental gradient methods for solving such problems, which use information about a single component function at each iteration. We provide new convergence rate results under some assumptions. We also consider incremental aggregated gradient methods, which compute a single component function gradient at each iteration while using outdated gradients of all component functions to approximate the entire global cost function, and provide new linear rate results.

This is joint work with Mert Gurbuzbalaban and Pablo Parrilo.

This is joint work with Mert Gurbuzbalaban and Pablo Parrilo.

Tuesday December 8, 2015 14:00 - 14:50

Level 2 room 210 AB

Level 2 room 210 AB

COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution

Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly intertwined stochastic processes, information diffusion and network evolution, have been predominantly studied separately, ignoring their co-evolutionary dynamics.We propose a temporal point process model, COEVOLVE, for such joint dynamics, allowing the intensity of one process to be modulated by that of the other. This model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks. Furthermore, we also develop a convex optimization framework to learn the parameters of the model from historical diffusion and network evolution traces. We experimented with both synthetic data and data gathered from Twitter, and show that our model provides a good fit to the data as well as more accurate predictions than alternatives.

Tuesday December 8, 2015 14:50 - 15:30

Room 210 A

Room 210 A

Probabilistic Line Searches for Stochastic Optimization

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic line search by combining the structure of existing deterministic methods with notions from Bayesian optimization. Our method retains a Gaussian process surrogate of the univariate optimization objective, and uses a probabilistic belief over the Wolfe conditions to monitor the descent. The algorithm has very low computational cost, and no user-controlled parameters. Experiments show that it effectively removes the need to define a learning rate for stochastic gradient descent.

Tuesday December 8, 2015 14:50 - 15:30

Room 210 A

Room 210 A

Automatic Variational Inference in Stan

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI); we implement it in Stan (code available), a probabilistic programming system. In ADVI the user provides a Bayesian model and a dataset, nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.

Tuesday December 8, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Data Generation as Sequential Decision Making

We connect a broad class of generative models through their shared reliance on sequential decision making. Motivated by this view, we develop extensions to an existing model, and then explore the idea further in the context of data imputation -- perhaps the simplest setting in which to investigate the relation between unconditional and conditional generative modelling. We formulate data imputation as an MDP and develop models capable of representing effective policies for it. We construct the models using neural networks and train them using a form of guided policy search. Our models generate predictions through an iterative process of feedback and refinement. We show that this approach can learn effective policies for imputation problems of varying difficulty and across multiple datasets.

Tuesday December 8, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Deep learning with Elastic Averaging SGD

We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of communication between local workers and the master. We empirically demonstrate that in the deep learning setting, due to the existence of many local optima, allowing more exploration can lead to the improved performance. We propose synchronous and asynchronous variants of the new algorithm. We provide the stability analysis of the asynchronous variant in the round-robin scheme and compare it with the more common parallelized method ADMM. We show that the stability of EASGD is guaranteed when a simple stability condition is satisfied, which is not the case for ADMM. We additionally propose the momentum-based version of our algorithm that can be applied in both synchronous and asynchronous settings. Asynchronous variant of the algorithm is applied to train convolutional neural networks for image classification on the CIFAR and ImageNet datasets. Experiments demonstrate that the new algorithm accelerates the training of deep architectures compared to DOWNPOUR and other common baseline approaches and furthermore is very communication efficient.

Tuesday December 8, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Latent Bayesian melding for integrating individual and population models

In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matchingexpectations between two models, but sometimes both models are most conveniently expressed as latent variable models. We propose latent Bayesian melding, which is motivated by averaging the distributions over populations statistics of both the individual-level and the population-level models under a logarithmic opinion pool framework. In a case study on electricity disaggregation, which is a type of single-channel blind source separation problem, we show that latent Bayesian melding leads to significantly more accurate predictions than an approach based solely on generalized moment matching.

Tuesday December 8, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Linear Response Methods for Accurate Covariance Estimates from Mean Field Variational Bayes

Mean field variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, a well known failing of MFVB is that it underestimates the uncertainty of model variables (sometimes severely) and provides no information about model variable covariance. We generalize linear response methods from statistical physics to deliver accurate uncertainty estimates for model variables---both for individual variables and coherently across variables. We call our method linear response variational Bayes (LRVB). When the MFVB posterior approximation is in the exponential family, LRVB has a simple, analytic form, even for non-conjugate models. Indeed, we make no assumptions about the form of the true posterior. We demonstrate the accuracy and scalability of our method on a range of models for both simulated and real data.

Tuesday December 8, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width

Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width. We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates, which have bounded hierarchy width—regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers.

Tuesday December 8, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Stochastic Expectation Propagation

Expectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local-approximations that are iteratively refined for each datapoint. EP can offer analytic and computational advantages over other approximations, such as Variational Inference (VI), and is the method of choice for a number of models. The local nature of EP appears to make it an ideal candidate for performing Bayesian learning on large models in large-scale datasets settings. However, EP has a crucial limitation in this context: the number approximating factors needs to increase with the number of data-points, N, which often entails a prohibitively large memory overhead. This paper presents an extension to EP, called stochastic expectation propagation (SEP), that maintains a global posterior approximation (like VI) but updates it in a local way (like EP). Experiments on a number of canonical learning problems using synthetic and real-world datasets indicate that SEP performs almost as well as full EP, but reduces the memory consumption by a factor of N. SEP is therefore ideally suited to performing approximate Bayesian learning in the large model, large dataset setting.

Tuesday December 8, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Competitive Distribution Estimation: Why is Good-Turing Good

Estimating distributions over large alphabets is a fundamental machine-learning tenet. Yet no method is known to estimate all distributions well. For example, add-constant estimators are nearly min-max optimal but often perform poorly in practice, and practical estimators such as absolute discounting, Jelinek-Mercer, and Good-Turing are not known to be near optimal for essentially any distribution.We describe the first universally near-optimal probability estimators. For every discrete distribution, they are provably nearly the best in the following two competitive ways. First they estimate every distribution nearly as well as the best estimator designed with prior knowledge of the distribution up to a permutation. Second, they estimate every distribution nearly as well as the best estimator designed with prior knowledge of the exact distribution, but as all natural estimators, restricted to assign the same probability to all symbols appearing the same number of times.Specifically, for distributions over $k$ symbols and $n$ samples, we show that for both comparisons, a simple variant of Good-Turing estimator is always within KL divergence of $(3+o(1))/n^{1/3}$ from the best estimator, and that a more involved estimator is within $\tilde{\mathcal{O}}(\min(k/n,1/\sqrt n))$. Conversely, we show that any estimator must have a KL divergence $\ge\tilde\Omega(\min(k/n,1/ n^{2/3}))$ over the best estimator for the first comparison, and $\ge\tilde\Omega(\min(k/n,1/\sqrt{n}))$ for the second.

Tuesday December 8, 2015 16:30 - 17:30

Room 210 A

Room 210 A

Fast Convergence of Regularized Learning in Games

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in a game uses an algorithm from our class, their individual regret decays at $O(T^{-3/4})$, while the sum of utilities converges to an approximate optimum at $O(T^{-1})$--an improvement upon the worst case $O(T^{-1/2})$ rates. We show a black-box reduction for any algorithm in the class to achieve $\tilde{O}(T^{-1/2})$ rates against an adversary, while maintaining the faster rates against algorithms in the class. Our results extend those of Rakhlin and Shridharan~\cite{Rakhlin2013} and Daskalakis et al.~\cite{Daskalakis2014}, who only analyzed two-player zero-sum games for specific algorithms.

Tuesday December 8, 2015 16:30 - 17:30

Room 210 A

Room 210 A

Interactive Control of Diverse Complex Characters with Neural Networks

We present a method for training recurrent neural networks to act as near-optimal feedback controllers. It is able to generate stable and realistic behaviors for a range of dynamical systems and tasks -- swimming, flying, biped and quadruped walking with different body morphologies. It does not require motion capture or task-specific features or state machines. The controller is a neural network, having a large number of feed-forward units that learn elaborate state-action mappings, and a small number of recurrent units that implement memory states beyond the physical system state. The action generated by the network is defined as velocity. Thus the network is not learning a control policy, but rather the dynamics under an implicit policy. Essential features of the method include interleaving supervised learning with trajectory optimization, injecting noise during training, training for unexpected changes in the task specification, and using the trajectory optimizer to obtain optimal feedback gains in addition to optimal actions.

Tuesday December 8, 2015 16:30 - 17:30

Room 210 A

Room 210 A

Biologically Inspired Dynamic Textures for Probing Motion Perception

Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative model specifically crafted to probe motion perception. In that context, we first provide an axiomatic, biologically-driven derivation of the model. This model synthesizes random dynamic textures which are defined by stationary Gaussian distributions obtained by the random aggregation of warped patterns. Importantly, we show that this model can equivalently be described as a stochastic partial differential equation. Using this characterization of motion in images, it allows us to recast motion-energy models into a principled Bayesian inference framework. Finally, we apply these textures in order to psychophysically probe speed perception in humans. In this framework, while the likelihood is derived from the generative model, the prior is estimated from the observed results and accounts for the perceptual bias in a principled fashion.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

Closed-form Estimators for High-dimensional Generalized Linear Models

We propose a class of closed-form estimators for GLMs under high-dimensional sampling regimes. Our class of estimators is based on deriving closed-form variants of the vanilla unregularized MLE but which are (a) well-defined even under high-dimensional settings, and (b) available in closed-form. We then perform thresholding operations on this MLE variant to obtain our class of estimators. We derive a unified statistical analysis of our class of estimators, and show that it enjoys strong statistical guarantees in both parameter error as well as variable selection, that surprisingly match those of the more complex regularized GLM MLEs, even while our closed-form estimators are computationally much simpler. We derive instantiations of our class of closed-form estimators, as well as corollaries of our general theorem, for the special cases of logistic, exponential and Poisson regression models. We corroborate the surprising statistical and computational performance of our class of estimators via extensive simulations.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

High-dimensional neural spike train analysis with generalized count linear dynamical systems

Latent factor models have been widely used to analyze simultaneous recordings of spike trains from large, heterogeneous neural populations. These models assume the signal of interest in the population is a low-dimensional latent intensity that evolves over time, which is observed in high dimension via noisy point-process observations. These techniques have been well used to capture neural correlations across a population and to provide a smooth, denoised, and concise representation of high-dimensional spiking data. One limitation of many current models is that the observation model is assumed to be Poisson, which lacks the flexibility to capture under- and over-dispersion that is common in recorded neural data, thereby introducing bias into estimates of covariance. Here we develop the generalized count linear dynamical system, which relaxes the Poisson assumption by using a more general exponential family for count data. In addition to containing Poisson, Bernoulli, negative binomial, and other common count distributions as special cases, we show that this model can be tractably learned by extending recent advances in variational inference techniques. We apply our model to data from primate motor cortex and demonstrate performance improvements over state-of-the-art methods, both in capturing the variance structure of the data and in held-out prediction.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

Large-Scale Bayesian Multi-Label Learning via Topic-Based Label Embeddings

We present a scalable Bayesian multi-label learning model based on learning low-dimensional label embeddings. Our model assumes that each label vector is generated as a weighted combination of a set of topics (each topic being a distribution over labels), where the combination weights (i.e., the embeddings) for each label vector are conditioned on the observed feature vector. This construction, coupled with a Bernoulli-Poisson link function for each label of the binary label vector, leads to a model with a computational cost that scales in the number of positive labels in the label matrix. This makes the model particularly appealing for real-world multi-label learning problems where the label matrix is usually very massive but highly sparse. Using a data-augmentation strategy leads to full local conjugacy in our model, facilitating simple and very efficient Gibbs sampling, as well as an Expectation Maximization algorithm for inference. Also, predicting the label vector at test time does not require doing an inference for the label embeddings and can be done in closed form. We report results on several benchmark data sets, comparing our model with various state-of-the art methods.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

Learning Stationary Time Series using Gaussian Processes with Nonparametric Kernels

We introduce the Gaussian Process Convolution Model (GPCM), a two-stage nonparametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise process and a continuous-time linear filter drawn from Gaussian process. The GPCM is a continuous-time nonparametric-window moving average process and, conditionally, is itself a Gaussian process with a nonparametric kernel defined in a probabilistic fashion. The generative model can be equivalently considered in the frequency domain, where the power spectral density of the signal is specified using a Gaussian process. One of the main contributions of the paper is to develop a novel variational free-energy approach based on inter-domain inducing variables that efficiently learns the continuous-time linear filter and infers the driving white-noise process. In turn, this scheme provides closed-form probabilistic estimates of the covariance kernel and the noise-free signal both in denoising and prediction scenarios. Additionally, the variational inference procedure provides closed-form expressions for the approximate posterior of the spectral density given the observed data, leading to new Bayesian nonparametric approaches to spectrum estimation. The proposed GPCM is validated using synthetic and real-world signals.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

Measuring Sample Quality with Stein's Method

To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness creates new challenges for sampler and parameter selection, since standard measures of sample quality like effective sample size do not account for asymptotic bias. To address these challenges, we introduce a new computable quality measure based on Stein's method that bounds the discrepancy between sample and target expectations over a large class of test functions. We use our tool to compare exact, biased, and deterministic sample sequences and illustrate applications to hyperparameter selection, convergence rate assessment, and quantifying bias-variance tradeoffs in posterior inference.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

On the Pseudo-Dimension of Nearly Optimal Auctions

This paper develops a general approach, rooted in statistical learning theory, to learning an approximately revenue-maximizing auction from data. We introduce t-level auctions to interpolate between simple auctions, such as welfare maximization with reserve prices, and optimal auctions, thereby balancing the competing demands of expressivity and simplicity. We prove that such auctions have small representation error, in the sense that for every product distribution F over bidders’ valuations, there exists a t-level auction with small t and expected revenue close to optimal. We show that the set of t-level auctions has modest pseudo-dimension (for polynomial t) and therefore leads to small learning error. One consequence of our results is that, in arbitrary single-parameter settings, one can learn a mechanism with expected revenue arbitrarily close to optimal from a polynomial number of samples.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

The Human Kernel

Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating human expertise remains elusive; for example, Gaussian processes with standard kernels struggle on function extrapolation problems that are trivial for human learners. In this paper, we create function extrapolation problems and acquire human responses, and then design a kernel learning framework to reverse engineer the inductive biases of human learners across a set of behavioral experiments. We use the learned kernels to gain psychological insights and to extrapolate in human-like ways that go beyond traditional stationary and polynomial kernels. Finally, we investigate Occam's razor in human and Gaussian process based function learning.

Tuesday December 8, 2015 17:30 - 18:00

Room 210 A

Room 210 A

An interactive system for the extraction of meaningful visualizations from high-dimensional data

We demonstrate our novel techniques for building ensembles of low-dimensional projections that facilitate data understanding and visualization by human users, given a learning task such as classification or regression. Our system trains user-friendly models, called Informative Projection Ensembles (IPEs). Such ensembles comprise of a set of compact submodels that ensure compliance with stringent user-specified requirement on model size and complexity, in order to allow visualization of the extracted patterns from data. IPEs handle data in a query-specific manner, each sample being assigned to a specialized Informative Projection, with data being automatically partitioned during learning. Through this setup, the models attain high performance while maintaining the transparency and simplicity of low-dimensional classifiers and regressors.

In this demo, we illustrate how Informative Projection Ensembles were of great use in practical applications. Moreover, we allow users the possibility to train their own models in real time, specifying such settings as the number of submodels, the dimensionality of the subspaces, costs associated with features as well as the type of base classifier or regressor to be used. Users are also able to see the decision-support system in action, performing classification, regression or clustering on batches of test data. The process of handling test data is also transparent, with the system highlighting the selected submodel, and how the queries are assigned labels/values by the submodel itself. Users can give feedback to the system in terms of the assigned outputs, and they will be able to perform pairwise comparisons of the trained models.

We encourage participants to bring their own data to analyze. Users have the possibility of saving the outcome of the analysis, for their own datasets or non-proprietary ones. The system supports the csv format for data and xml for the models.

In this demo, we illustrate how Informative Projection Ensembles were of great use in practical applications. Moreover, we allow users the possibility to train their own models in real time, specifying such settings as the number of submodels, the dimensionality of the subspaces, costs associated with features as well as the type of base classifier or regressor to be used. Users are also able to see the decision-support system in action, performing classification, regression or clustering on batches of test data. The process of handling test data is also transparent, with the system highlighting the selected submodel, and how the queries are assigned labels/values by the submodel itself. Users can give feedback to the system in terms of the assigned outputs, and they will be able to perform pairwise comparisons of the trained models.

We encourage participants to bring their own data to analyze. Users have the possibility of saving the outcome of the analysis, for their own datasets or non-proprietary ones. The system supports the csv format for data and xml for the models.

Tuesday December 8, 2015 19:00 - 23:55

210D

210D

Claudico: The World's Strongest No-Limit Texas Hold'em Poker AI

Claudico is the world's strongest poker AI for two-player no-limit Texas Hold'em. Earlier this year, Claudico faced off against four of the top human poker players in the world in the Brains vs. AI man-machine competition for 80,000 hands of poker. Claudico is based on an earlier agent, Tartanian7, which won the latest Annual Computer Poker Competition, defeating all other agents with statistical significance.

This is the first poker AI to play at a competitive level with the very best humans in the world in no-limit Texas Hold'em, the most popular poker variant in the world. It is the result of over one million core hours, computed on the Blacklight supercomputer.

This is the first poker AI to play at a competitive level with the very best humans in the world in no-limit Texas Hold'em, the most popular poker variant in the world. It is the result of over one million core hours, computed on the Blacklight supercomputer.

Tuesday December 8, 2015 19:00 - 23:55

210D

210D

Deep Learning using Approximate Hardware

Title: Deep Learning using Approximate Hardware

Abstract:

We demo deep learning algorithms doing real-time vision on an "approximate computer". The machine is a prototype for embedded applications that provides 10x the compute per watt of a modern GPU. The technology allows a single (non-prototype) chip to contain 256,000 cores and to compute using 50x less energy that an equivalent GPU. A rack could hold 50 million cores, and accelerate deep learning training and other applications. The technology has been funded by DARPA (U.S.) and tested at MIT CSAIL, Carnegie Mellon, and elsewhere.

Abstract:

We demo deep learning algorithms doing real-time vision on an "approximate computer". The machine is a prototype for embedded applications that provides 10x the compute per watt of a modern GPU. The technology allows a single (non-prototype) chip to contain 256,000 cores and to compute using 50x less energy that an equivalent GPU. A rack could hold 50 million cores, and accelerate deep learning training and other applications. The technology has been funded by DARPA (U.S.) and tested at MIT CSAIL, Carnegie Mellon, and elsewhere.

Tuesday December 8, 2015 19:00 - 23:55

210D

210D

DIANNE - Distributed Artificial Neural Networks

In this demo users will be able to build neural networks using a drag & drop interface. Different neural network building blocks such as Convolutional, Linear, ReLu, Sigmoid, ... can be configured and connected to form a neural network. These networks can then be connected one of the supported Datasets (i.e. MNIST, CIFAR, ImageNet, ...) to evaluate the network accuracy, visualise the output for specific samples, or train a (small) network (for example in case of MNIST for immediate results). The users can also couple sensors and actuators to a neural network input/output, for example triggering a lamp based on classified camera input. The UI also allows to deploy the neural network building blocks on various different single-board platforms such as Raspberry Pi, Intel Edison and Nvidia Jetson and the difference in response time can be experienced.

Tuesday December 8, 2015 19:00 - 23:55

210D

210D

Fast sampling with neuromorphic hardware

Many of the problems that a typical brain is required to solve are of essentially Bayesian nature. How - or if at all - a Bayesian algorithm is embedded in the structure and dynamics of cortical neural networks remains the subject of considerable debate. Experimental evidence of a "Bayesian brain" has been steadily growing, as has the collection of models that have been put forward as possible candidates for a neuronal implementation of Bayesian inference.

The study of generative and discriminative models for various types of data is further bolstered by advances in fields that lie outside of neuroscience, but have obvious conceptual connections, such as machine learning and AI. Recent theoretical studies point towards a link between these models and biological neural networks.

Whether biological or not, all of these models are only as efficient as the physical substrate that they are embedded in allows them to be. Power efficiency as well as execution speed are of increasing importance as both the network models and their associated learning algorithms become large and/or complex. In our demo session, we will show the first implementation of neural sampling in mixed-signal, low-power and highly accelerated neuromorphic hardware. We will discuss the network structure and mechanisms by which we were able to counteract the imperfections that are inherent to the hardware manufacturing process and provide an interactive interface for users to manipulate the emulation parameters, in particular those of the target probability distribution from which the neuromorphic chip samples. The corresponding parameters of the on-chip spiking neural network can then either be calculated analytically or trained with simple learning rules. More advanced users which are familiar with spiking network simulators will be able to make use of the full versatility of the hardware substrate and program their own network models for neuromorphic emulation.

http://www.kip.uni-heidelberg.de/spikey

The study of generative and discriminative models for various types of data is further bolstered by advances in fields that lie outside of neuroscience, but have obvious conceptual connections, such as machine learning and AI. Recent theoretical studies point towards a link between these models and biological neural networks.

Whether biological or not, all of these models are only as efficient as the physical substrate that they are embedded in allows them to be. Power efficiency as well as execution speed are of increasing importance as both the network models and their associated learning algorithms become large and/or complex. In our demo session, we will show the first implementation of neural sampling in mixed-signal, low-power and highly accelerated neuromorphic hardware. We will discuss the network structure and mechanisms by which we were able to counteract the imperfections that are inherent to the hardware manufacturing process and provide an interactive interface for users to manipulate the emulation parameters, in particular those of the target probability distribution from which the neuromorphic chip samples. The corresponding parameters of the on-chip spiking neural network can then either be calculated analytically or trained with simple learning rules. More advanced users which are familiar with spiking network simulators will be able to make use of the full versatility of the hardware substrate and program their own network models for neuromorphic emulation.

http://www.kip.uni-heidelberg.de/spikey

Tuesday December 8, 2015 19:00 - 23:55

210D

210D

Vitruvian Science: a visual editor for quickly building neural networks in the cloud

We present a visual editor to make prototyping deep learning systems akin to building with Legos. This system allows you to visually depict architecture layouts (as you would on a whiteboard or scrap of paper) and compiles them to Theano functions running on the cloud. Our goal is to speed up development and debugging for novel deep learning architectures.

Tuesday December 8, 2015 19:00 - 23:55

210D

210D

A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements

We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random measurements of a positive semidefinite $n\times n$ matrix of rank $r$ and condition number $\kappa$, our method is guaranteed to converge linearly to the global optimum.

Tuesday December 8, 2015 19:00 - 23:59

210 C #93

210 C #93

A hybrid sampler for Poisson-Kingman mixture models

This paper concerns the introduction of a new Markov Chain Monte Carlo scheme for posterior sampling in Bayesian nonparametric mixture models with priors that belong to the general Poisson-Kingman class. We present a novel and compact way of representing the infinite dimensional component of the model such that while explicitly representing this infinite component it has less memory and storage requirements than previous MCMC schemes. We describe comparative simulation results demonstrating the efficacy of the proposed MCMC algorithm against existing marginal and conditional MCMC samplers.

Tuesday December 8, 2015 19:00 - 23:59

210 C #41

210 C #41

A Universal Primal-Dual Convex Optimization Framework

We propose a new primal-dual algorithmic framework for a prototypical constrained convex optimization template. The algorithmic instances of our framework are universal since they can automatically adapt to the unknown Holder continuity degree and constant within the dual formulation. They are also guaranteed to have optimal convergence rates in the objective residual and the feasibility gap for each Holder smoothness degree. In contrast to existing primal-dual algorithms, our framework avoids the proximity operator of the objective function. We instead leverage computationally cheaper, Fenchel-type operators, which are the main workhorses of the generalized conditional gradient (GCG)-type methods. In contrast to the GCG-type methods, our framework does not require the objective function to be differentiable, and can also process additional general linear inclusion constraints, while guarantees the convergence rate on the primal problem.

Tuesday December 8, 2015 19:00 - 23:59

210 C #89

210 C #89

Alternating Minimization for Regression Problems with Vector-valued Outputs

In regression problems involving vector-valued outputs (or equivalently, multiple responses), it is well known that the maximum likelihood estimator (MLE), which takes noise covariance structure into account, can be significantly more accurate than the ordinary least squares (OLS) estimator. However, existing literature compares OLS and MLE in terms of their asymptotic, not finite sample, guarantees. More crucially, computing the MLE in general requires solving a non-convex optimization problem and is not known to be efficiently solvable. We provide finite sample upper and lower bounds on the estimation error of OLS and MLE, in two popular models: a) Pooled model, b) Seemingly Unrelated Regression (SUR) model. We provide precise instances where the MLE is significantly more accurate than OLS. Furthermore, for both models, we show that the output of a computationally efficient alternating minimization procedure enjoys the same performance guarantee as MLE, up to universal constants. Finally, we show that for high-dimensional settings as well, the alternating minimization procedure leads to significantly more accurate solutions than the corresponding OLS solutions but with error bound that depends only logarithmically on the data dimensionality.

Tuesday December 8, 2015 19:00 - 23:59

210 C #76

210 C #76

Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization
The asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and speedup properties, mainly due to the nonconvexity of most deep learning formulations and the asynchronous parallel mechanism. To fill the gaps in theory and provide theoretical supports, this paper studies two asynchronous parallel implementations of SG: one is on the computer network and the other is on the shared memory system. We establish an ergodic convergence rate $O(1/\sqrt{K})$ for both algorithms and prove that the linear speedup is achievable if the number of workers is bounded by $\sqrt{K}$ ($K$ is the total number of iterations). Our results generalize and improve existing analysis for convex minimization.

Tuesday December 8, 2015 19:00 - 23:59

210 C #63

210 C #63

Automatic Variational Inference in Stan
Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI); we implement it in Stan (code available), a probabilistic programming system. In ADVI the user provides a Bayesian model and a dataset, nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.

Tuesday December 8, 2015 19:00 - 23:59

210 C #34

210 C #34

b-bit Marginal Regression
We consider the problem of sparse signal recovery from $m$ linear measurements quantized to $b$ bits. $b$-bit Marginal Regression is proposed as recovery algorithm. We study the question of choosing $b$ in the setting of a given budget of bits $B = m \cdot b$ and derive a single easy-to-compute expression characterizing the trade-off between $m$ and $b$. The choice $b = 1$ turns out to be optimal for estimating the unit vector corresponding to the signal for any level of additive Gaussian noise before quantization as well as for adversarial noise. For $b \geq 2$, we show that Lloyd-Max quantization constitutes an optimal quantization scheme and that the norm of the signal canbe estimated consistently by maximum likelihood.

Tuesday December 8, 2015 19:00 - 23:59

210 C #81

210 C #81

Bidirectional Recurrent Convolutional Networks for Multi-Frame Super-Resolution

Super resolving a low-resolution video is usually handled by either single-image super-resolution (SR) or multi-frame SR. Single-Image SR deals with each video frame independently, and ignores intrinsic temporal dependency of video frames which actually plays a very important role in video super-resolution. Multi-Frame SR generally extracts motion information, e.g. optical flow, to model the temporal dependency, which often shows high computational cost. Considering that recurrent neural network (RNN) can model long-term contextual information of temporal sequences well, we propose a bidirectional recurrent convolutional network for efficient multi-frame SR.Different from vanilla RNN, 1) the commonly-used recurrent full connections are replaced with weight-sharing convolutional connections and 2) conditional convolutional connections from previous input layers to current hidden layer are added for enhancing visual-temporal dependency modelling. With the powerful temporal dependency modelling, our model can super resolve videos with complex motions and achieve state-of-the-art performance. Due to the cheap convolution operations, our model has a low computational complexity and runs orders of magnitude faster than other multi-frame methods.

Tuesday December 8, 2015 19:00 - 23:59

210 C #6

210 C #6

Biologically Inspired Dynamic Textures for Probing Motion Perception
Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative model specifically crafted to probe motion perception. In that context, we first provide an axiomatic, biologically-driven derivation of the model. This model synthesizes random dynamic textures which are defined by stationary Gaussian distributions obtained by the random aggregation of warped patterns. Importantly, we show that this model can equivalently be described as a stochastic partial differential equation. Using this characterization of motion in images, it allows us to recast motion-energy models into a principled Bayesian inference framework. Finally, we apply these textures in order to psychophysically probe speed perception in humans. In this framework, while the likelihood is derived from the generative model, the prior is estimated from the observed results and accounts for the perceptual bias in a principled fashion.

Tuesday December 8, 2015 19:00 - 23:59

210 C #14

210 C #14

Character-level Convolutional Networks for Text Classification

This article offers an empirical exploration on the use of character-level convolutional networks (ConvNets) for text classification. We constructed several large-scale datasets to show that character-level convolutional networks could achieve state-of-the-art or competitive results. Comparisons are offered against traditional models such as bag of words, n-grams and their TFIDF variants, and deep learning models such as word-based ConvNets and recurrent neural networks.

Tuesday December 8, 2015 19:00 - 23:59

210 C #10

210 C #10

Closed-form Estimators for High-dimensional Generalized Linear Models
We propose a class of closed-form estimators for GLMs under high-dimensional sampling regimes. Our class of estimators is based on deriving closed-form variants of the vanilla unregularized MLE but which are (a) well-defined even under high-dimensional settings, and (b) available in closed-form. We then perform thresholding operations on this MLE variant to obtain our class of estimators. We derive a unified statistical analysis of our class of estimators, and show that it enjoys strong statistical guarantees in both parameter error as well as variable selection, that surprisingly match those of the more complex regularized GLM MLEs, even while our closed-form estimators are computationally much simpler. We derive instantiations of our class of closed-form estimators, as well as corollaries of our general theorem, for the special cases of logistic, exponential and Poisson regression models. We corroborate the surprising statistical and computational performance of our class of estimators via extensive simulations.

Tuesday December 8, 2015 19:00 - 23:59

210 C #85

210 C #85

COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution
Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly intertwined stochastic processes, information diffusion and network evolution, have been predominantly studied separately, ignoring their co-evolutionary dynamics.We propose a temporal point process model, COEVOLVE, for such joint dynamics, allowing the intensity of one process to be modulated by that of the other. This model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks. Furthermore, we also develop a convex optimization framework to learn the parameters of the model from historical diffusion and network evolution traces. We experimented with both synthetic data and data gathered from Twitter, and show that our model provides a good fit to the data as well as more accurate predictions than alternatives.

Tuesday December 8, 2015 19:00 - 23:59

210 C #23

210 C #23

Collaboratively Learning Preferences from Ordinal Data

In personalized recommendation systems, it is important to predict preferences of a user on items that have not been seen by that user yet. Similarly, in revenue management, it is important to predict outcomes of comparisons among those items that have never been compared so far. The MultiNomial Logit model, a popular discrete choice model, captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to solve a convex relaxation of nuclear norm minimization. We present the convex relaxation approach in two contexts of interest: collaborative ranking and bundled choice modeling. In both cases, we show that the convex relaxation is minimax optimal. We prove an upper bound on the resulting error with finite samples, and provide a matching information-theoretic lower bound.

Tuesday December 8, 2015 19:00 - 23:59

210 C #74

210 C #74

Combinatorial Bandits Revisited

This paper investigates stochastic and adversarial combinatorial multi-armed bandit problems. In the stochastic setting under semi-bandit feedback, we derive a problem-specific regret lower bound, and discuss its scaling with the dimension of the decision space. We propose ESCB, an algorithm that efficiently exploits the structure of the problem and provide a finite-time analysis of its regret. ESCB has better performance guarantees than existing algorithms, and significantly outperforms these algorithms in practice. In the adversarial setting under bandit feedback, we propose CombEXP, an algorithm with the same regret scaling as state-of-the-art algorithms, but with lower computational complexity for some combinatorial problems.

Tuesday December 8, 2015 19:00 - 23:59

210 C #96

210 C #96

Community Detection via Measure Space Embedding

We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of $k$-means in that space is applied. The algorithm is therefore fast and easily parallelizable. We evaluate the algorithm on standard random graph benchmarks, including some overlapping community benchmarks, and find its performance to be better or at least as good as previously known algorithms. We also prove a linear time (in number of edges) guarantee for the algorithm on a $p,q$-stochastic block model with where $p \geq c\cdot N^{-\half + \epsilon}$ and $p-q \geq c' \sqrt{p N^{-\half + \epsilon} \log N}$.

Tuesday December 8, 2015 19:00 - 23:59

210 C #52

210 C #52

Competitive Distribution Estimation: Why is Good-Turing Good
Estimating distributions over large alphabets is a fundamental machine-learning tenet. Yet no method is known to estimate all distributions well. For example, add-constant estimators are nearly min-max optimal but often perform poorly in practice, and practical estimators such as absolute discounting, Jelinek-Mercer, and Good-Turing are not known to be near optimal for essentially any distribution.We describe the first universally near-optimal probability estimators. For every discrete distribution, they are provably nearly the best in the following two competitive ways. First they estimate every distribution nearly as well as the best estimator designed with prior knowledge of the distribution up to a permutation. Second, they estimate every distribution nearly as well as the best estimator designed with prior knowledge of the exact distribution, but as all natural estimators, restricted to assign the same probability to all symbols appearing the same number of times.Specifically, for distributions over $k$ symbols and $n$ samples, we show that for both comparisons, a simple variant of Good-Turing estimator is always within KL divergence of $(3+o(1))/n^{1/3}$ from the best estimator, and that a more involved estimator is within $\tilde{\mathcal{O}}(\min(k/n,1/\sqrt n))$. Conversely, we show that any estimator must have a KL divergence $\ge\tilde\Omega(\min(k/n,1/ n^{2/3}))$ over the best estimator for the first comparison, and $\ge\tilde\Omega(\min(k/n,1/\sqrt{n}))$ for the second.

Tuesday December 8, 2015 19:00 - 23:59

210 C #88

210 C #88

Data Generation as Sequential Decision Making
We connect a broad class of generative models through their shared reliance on sequential decision making. Motivated by this view, we develop extensions to an existing model, and then explore the idea further in the context of data imputation -- perhaps the simplest setting in which to investigate the relation between unconditional and conditional generative modelling. We formulate data imputation as an MDP and develop models capable of representing effective policies for it. We construct the models using neural networks and train them using a form of guided policy search. Our models generate predictions through an iterative process of feedback and refinement. We show that this approach can learn effective policies for imputation problems of varying difficulty and across multiple datasets.

Tuesday December 8, 2015 19:00 - 23:59

210 C #35

210 C #35

Deep Generative Image Models using a ￼Laplacian Pyramid of Adversarial Networks

In this paper we introduce a generative model capable of producing high quality samples of natural images. Our approach uses a cascade of convolutional networks (convnets) within a Laplacian pyramid framework to generate images in a coarse-to-fine fashion. At each level of the pyramid a separate generative convnet model is trained using the Generative Adversarial Nets (GAN) approach. Samples drawn from our model are of significantly higher quality than existing models. In a quantitive assessment by human evaluators our CIFAR10 samples were mistaken for real images around 40% of the time, compared to 10% for GAN samples. We also show samples from more diverse datasets such as STL10 and LSUN.

Tuesday December 8, 2015 19:00 - 23:59

210 C #1

210 C #1

Deep learning with Elastic Averaging SGD
We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of communication between local workers and the master. We empirically demonstrate that in the deep learning setting, due to the existence of many local optima, allowing more exploration can lead to the improved performance. We propose synchronous and asynchronous variants of the new algorithm. We provide the stability analysis of the asynchronous variant in the round-robin scheme and compare it with the more common parallelized method ADMM. We show that the stability of EASGD is guaranteed when a simple stability condition is satisfied, which is not the case for ADMM. We additionally propose the momentum-based version of our algorithm that can be applied in both synchronous and asynchronous settings. Asynchronous variant of the algorithm is applied to train convolutional neural networks for image classification on the CIFAR and ImageNet datasets. Experiments demonstrate that the new algorithm accelerates the training of deep architectures compared to DOWNPOUR and other common baseline approaches and furthermore is very communication efficient.

Tuesday December 8, 2015 19:00 - 23:59

210 C #37

210 C #37

Deep Poisson Factor Modeling

We propose a new deep architecture for topic modeling, based on Poisson Factor Analysis (PFA) modules. The model is composed of a Poisson distribution to model observed vectors of counts, as well as a deep hierarchy of hidden binary units. Rather than using logistic functions to characterize the probability that a latent binary unit is on, we employ a Bernoulli-Poisson link, which allows PFA modules to be used repeatedly in the deep architecture. We also describe an approach to build discriminative topic models, by adapting PFA modules. We derive efficient inference via MCMC and stochastic variational methods, that scale with the number of non-zeros in the data and binary units, yielding significant efficiency, relative to models based on logistic links. Experiments on several corpora demonstrate the advantages of our model when compared to related deep models.

Tuesday December 8, 2015 19:00 - 23:59

210 C #16

210 C #16

Deeply Learning the Messages in Message Passing Inference

Deep structured output learning shows great promise in tasks like semantic image segmentation. We proffer a new, efficient deep structured model learning scheme, in which we show how deep Convolutional Neural Networks (CNNs) can be used to directly estimate the messages in message passing inference for structured prediction with Conditional Random Fields CRFs). With such CNN message estimators, we obviate the need to learn or evaluate potential functions for message calculation. This confers significant efficiency for learning, since otherwise when performing structured learning for a CRF with CNN potentials it is necessary to undertake expensive inference for every stochastic gradient iteration. The network output dimension of message estimators is the same as the number of classes, rather than exponentially growing in the order of the potentials. Hence it is more scalable for cases that a large number of classes are involved. We apply our method to semantic image segmentation and achieve impressive performance, which demonstrates the effectiveness and usefulness of our CNN message learning method.

Tuesday December 8, 2015 19:00 - 23:59

210 C #22

210 C #22

Distributed Submodular Cover: Succinctly Summarizing Massive Data
How can one find a subset, ideally as small as possible, that well represents a massive dataset? I.e., its corresponding utility, measured according to a suitable utility function, should be comparable to that of the whole dataset. In this paper, we formalize this challenge as a submodular cover problem. Here, the utility is assumed to exhibit submodularity, a natural diminishing returns condition preva- lent in many data summarization applications. The classical greedy algorithm is known to provide solutions with logarithmic approximation guarantees compared to the optimum solution. However, this sequential, centralized approach is imprac- tical for truly large-scale problems. In this work, we develop the first distributed algorithm – DISCOVER – for submodular set cover that is easily implementable using MapReduce-style computations. We theoretically analyze our approach, and present approximation guarantees for the solutions returned by DISCOVER. We also study a natural trade-off between the communication cost and the num- ber of rounds required to obtain such a solution. In our extensive experiments, we demonstrate the effectiveness of our approach on several applications, includ- ing active set selection, exemplar based clustering, and vertex cover on tens of millions of data points using Spark.

Tuesday December 8, 2015 19:00 - 23:59

210 C #65

210 C #65

Distributionally Robust Logistic Regression
This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this Wasserstein ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high confidence. We then formulate a distributionally robust logistic regression model that minimizes a worst-case expected logloss function, where the worst case is taken over all distributions in the Wasserstein ball. We prove that this optimization problem admits a tractable reformulation and encapsulates the classical as well as the popular regularized logistic regression problems as special cases. We further propose a distributionally robust approach based on Wasserstein balls to compute upper and lower confidence bounds on the misclassification probability of the resulting classifier. These bounds are given by the optimal values of two highly tractable linear programs. We validate our theoretical out-of-sample guarantees through simulated and empirical experiments.

Tuesday December 8, 2015 19:00 - 23:59

210 C #60

210 C #60

Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer's disease dataset.

Tuesday December 8, 2015 19:00 - 23:59

210 C #27

210 C #27

Evaluating the statistical significance of biclusters

Biclustering (also known as submatrix localization) is a problem of high practical relevance in exploratory analysis of high-dimensional data. We develop a framework for performing statistical inference on biclusters found by score-based algorithms. Since the bicluster was selected in a data dependent manner by a biclustering or localization algorithm, this is a form of selective inference. Our framework gives exact (non-asymptotic) confidence intervals and p-values for the significance of the selected biclusters. Further, we generalize our approach to obtain exact inference for Gaussian statistics.

Tuesday December 8, 2015 19:00 - 23:59

210 C #68

210 C #68

Expressing an Image Stream with a Sequence of Natural Sentences

We propose an approach for generating a sequence of natural sentences for an image stream. Since general users usually take a series of pictures on their special moments, much online visual information exists in the form of image streams, for which it would better take into consideration of the whole set to generate natural language descriptions. While almost all previous studies have dealt with the relation between a single image and a single natural sentence, our work extends both input and output dimension to a sequence of images and a sequence of sentences. To this end, we design a novel architecture called coherent recurrent convolutional network (CRCN), which consists of convolutional networks, bidirectional recurrent networks, and entity-based local coherence model. Our approach directly learns from vast user-generated resource of blog posts as text-image parallel training data. We demonstrate that our approach outperforms other state-of-the-art candidate methods, using both quantitative measures (e.g. BLEU and top-K recall) and user studies via Amazon Mechanical Turk.

Tuesday December 8, 2015 19:00 - 23:59

210 C #4

210 C #4

Extending Gossip Algorithms to Distributed Estimation of U-statistics
Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of U-statistics, relying on more expensive averaging over pairs of observations, is a less investigated area. Yet, such data functionals are essential to describe global properties of a statistical population, with important examples including Area Under the Curve, empirical variance, Gini mean difference and within-cluster point scatter. This paper proposes new synchronous and asynchronous randomized gossip algorithms which simultaneously propagate data across the network and maintain local estimates of the U-statistic of interest. We establish convergence rate bounds of O(1 / t) and O(log t / t) for the synchronous and asynchronous cases respectively, where t is the number of iterations, with explicit data and network dependent terms. Beyond favorable comparisons in terms of rate analysis, numerical experiments provide empirical evidence the proposed algorithms surpasses the previously introduced approach.

Tuesday December 8, 2015 19:00 - 23:59

210 C #72

210 C #72

Fast Bidirectional Probability Estimation in Markov Models

We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given source distribution. Given the target state $t$, we use a (reverse) local power iteration to construct an `expanded target distribution', which has the same mean as the quantity we want to estimate, but a smaller variance -- this can then be sampled efficiently by a Monte Carlo algorithm. Our method extends to any Markov chain on a discrete (finite or countable) state-space, and can be extended to compute functions of multi-step transition probabilities such as PageRank, graph diffusions, hitting/return times, etc. Our main result is that in `sparse' Markov Chains -- wherein the number of transitions between states is comparable to the number of states -- the running time of our algorithm for a uniform-random target node is order-wise smaller than Monte Carlo and power iteration based algorithms; in particular, our method can estimate a probability $p$ using only $O(1/\sqrt{p})$ running time.

Tuesday December 8, 2015 19:00 - 23:59

210 C #67

210 C #67

Fast Convergence of Regularized Learning in Games
We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in a game uses an algorithm from our class, their individual regret decays at $O(T^{-3/4})$, while the sum of utilities converges to an approximate optimum at $O(T^{-1})$--an improvement upon the worst case $O(T^{-1/2})$ rates. We show a black-box reduction for any algorithm in the class to achieve $\tilde{O}(T^{-1/2})$ rates against an adversary, while maintaining the faster rates against algorithms in the class. Our results extend those of Rakhlin and Shridharan~\cite{Rakhlin2013} and Daskalakis et al.~\cite{Daskalakis2014}, who only analyzed two-player zero-sum games for specific algorithms.

Tuesday December 8, 2015 19:00 - 23:59

210 C #97

210 C #97

Fast, Provable Algorithms for Isotonic Regression in all L_p-norms

Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices, the Isotonic Regression of $y$ is a vector $x$ that respects the partial order described by $G,$ and minimizes $\|x-y\|,$ for a specified norm. This paper gives improved algorithms for computing the Isotonic Regression for all weighted $\ell_{p}$-norms with rigorous performance guarantees. Our algorithms are quite practical, and their variants can be implemented to run fast in practice.

Tuesday December 8, 2015 19:00 - 23:59

210 C #86

210 C #86

Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees
There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. An important challenge is to reconcile these probabilistic integrators with rigorous convergence guarantees. In this paper, we present the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ). Under FWBQ, convergence to the true value of the integral is shown to be exponential and posterior contraction rates are proven to be superexponential. In simulations, FWBQ is competitive with state-of-the-art methods and out-performs alternatives based on Frank-Wolfe optimisation. Our approach is applied to successfully quantify numerical error in the solution to a challenging model choice problem in cellular biology.

Tuesday December 8, 2015 19:00 - 23:59

210 C #57

210 C #57

Galileo: Perceiving Physical Object Properties by Integrating a Physics Engine with Deep Learning

Humans demonstrate remarkable abilities to predict physical events in dynamic scenes, and to infer the physical properties of objects from static images. We propose a generative model for solving these problems of physical scene understanding from real-world videos and images. At the core of our generative model is a 3D physics engine, operating on an object-based representation of physical properties, including mass, position, 3D shape, and friction. We can infer these latent properties using relatively brief runs of MCMC, which drive simulations in the physics engine to fit key features of visual observations. We further explore directly mapping visual inputs to physical properties, inverting a part of the generative process using deep learning. We name our model Galileo, and evaluate it on a video dataset with simple yet physically rich scenarios. Results show that Galileo is able to infer the physical properties of objects and predict the outcome of a variety of physical events, with an accuracy comparable to human subjects. Our study points towards an account of human vision with generative physical knowledge at its core, and various recognition models as helpers leading to efficient inference.

Tuesday December 8, 2015 19:00 - 23:59

210 C #8

210 C #8

High-dimensional neural spike train analysis with generalized count linear dynamical systems
Latent factor models have been widely used to analyze simultaneous recordings of spike trains from large, heterogeneous neural populations. These models assume the signal of interest in the population is a low-dimensional latent intensity that evolves over time, which is observed in high dimension via noisy point-process observations. These techniques have been well used to capture neural correlations across a population and to provide a smooth, denoised, and concise representation of high-dimensional spiking data. One limitation of many current models is that the observation model is assumed to be Poisson, which lacks the flexibility to capture under- and over-dispersion that is common in recorded neural data, thereby introducing bias into estimates of covariance. Here we develop the generalized count linear dynamical system, which relaxes the Poisson assumption by using a more general exponential family for count data. In addition to containing Poisson, Bernoulli, negative binomial, and other common count distributions as special cases, we show that this model can be tractably learned by extending recent advances in variational inference techniques. We apply our model to data from primate motor cortex and demonstrate performance improvements over state-of-the-art methods, both in capturing the variance structure of the data and in held-out prediction.

Tuesday December 8, 2015 19:00 - 23:59

210 C #26

210 C #26

HONOR: Hybrid Optimization for NOn-convex Regularized problems

Recent years have witnessed the superiority of non-convex sparse learning formulations over their convex counterparts in both theory and practice. However, due to the non-convexity and non-smoothness of the regularizer, how to efficiently solve the non-convex optimization problem for large-scale data is still quite challenging. In this paper, we propose an efficient \underline{H}ybrid \underline{O}ptimization algorithm for \underline{NO}n convex \underline{R}egularized problems (HONOR). Specifically, we develop a hybrid scheme which effectively integrates a Quasi-Newton (QN) step and a Gradient Descent (GD) step. Our contributions are as follows: (1) HONOR incorporates the second-order information to greatly speed up the convergence, while it avoids solving a regularized quadratic programming and only involves matrix-vector multiplications without explicitly forming the inverse Hessian matrix. (2) We establish a rigorous convergence analysis for HONOR, which shows that convergence is guaranteed even for non-convex problems, while it is typically challenging to analyze the convergence for non-convex problems. (3) We conduct empirical studies on large-scale data sets and results demonstrate that HONOR converges significantly faster than state-of-the-art algorithms.

Tuesday December 8, 2015 19:00 - 23:59

210 C #92

210 C #92

Inference for determinantal point processes without spectral knowledge

Determinantal point processes (DPPs) are point process models thatnaturally encode diversity between the points of agiven realization, through a positive definite kernel $K$. DPPs possess desirable properties, such as exactsampling or analyticity of the moments, but learning the parameters ofkernel $K$ through likelihood-based inference is notstraightforward. First, the kernel that appears in thelikelihood is not $K$, but another kernel $L$ related to $K$ throughan often intractable spectral decomposition. This issue is typically bypassed in machine learning bydirectly parametrizing the kernel $L$, at the price of someinterpretability of the model parameters. We follow this approachhere. Second, the likelihood has an intractable normalizingconstant, which takes the form of large determinant in the case of aDPP over a finite set of objects, and the form of a Fredholm determinant in thecase of a DPP over a continuous domain. Our main contribution is to derive bounds on the likelihood ofa DPP, both for finite and continuous domains. Unlike previous work, our bounds arecheap to evaluate since they do not rely on approximating the spectrumof a large matrix or an operator. Through usual arguments, these bounds thus yield cheap variationalinference and moderately expensive exact Markov chain Monte Carlo inference methods for DPPs.

Tuesday December 8, 2015 19:00 - 23:59

210 C #54

210 C #54

Interactive Control of Diverse Complex Characters with Neural Networks
We present a method for training recurrent neural networks to act as near-optimal feedback controllers. It is able to generate stable and realistic behaviors for a range of dynamical systems and tasks -- swimming, flying, biped and quadruped walking with different body morphologies. It does not require motion capture or task-specific features or state machines. The controller is a neural network, having a large number of feed-forward units that learn elaborate state-action mappings, and a small number of recurrent units that implement memory states beyond the physical system state. The action generated by the network is defined as velocity. Thus the network is not learning a control policy, but rather the dynamics under an implicit policy. Essential features of the method include interleaving supervised learning with trajectory optimization, injecting noise during training, training for unexpected changes in the task specification, and using the trajectory optimizer to obtain optimal feedback gains in addition to optimal actions.

Tuesday December 8, 2015 19:00 - 23:59

210 C #13

210 C #13

Interpolating Convex and Non-Convex Tensor Decompositions via the Subspace Norm

We consider the problem of recovering a low-rank tensor from its noisy observation. Previous work has shown a recovery guarantee with signal to noise ratio $O(n^{\ceil{K/2}/2})$ for recovering a $K$th order rank one tensor of size $n\times \cdots \times n$ by recursive unfolding. In this paper, we first improve this bound to $O(n^{K/4})$ by a much simpler approach, but with a more careful analysis. Then we propose a new norm called the \textit{subspace} norm, which is based on the Kronecker products of factors obtained by the proposed simple estimator. The imposed Kronecker structure allows us to show a nearly ideal $O(\sqrt{n}+\sqrt{H^{K-1}})$ bound, in which the parameter $H$ controls the blend from the non-convex estimator to mode-wise nuclear norm minimization. Furthermore, we empirically demonstrate that the subspace norm achieves the nearly ideal denoising performance even with $H=O(1)$.

Tuesday December 8, 2015 19:00 - 23:59

210 C #79

210 C #79

Large-Scale Bayesian Multi-Label Learning via Topic-Based Label Embeddings
We present a scalable Bayesian multi-label learning model based on learning low-dimensional label embeddings. Our model assumes that each label vector is generated as a weighted combination of a set of topics (each topic being a distribution over labels), where the combination weights (i.e., the embeddings) for each label vector are conditioned on the observed feature vector. This construction, coupled with a Bernoulli-Poisson link function for each label of the binary label vector, leads to a model with a computational cost that scales in the number of positive labels in the label matrix. This makes the model particularly appealing for real-world multi-label learning problems where the label matrix is usually very massive but highly sparse. Using a data-augmentation strategy leads to full local conjugacy in our model, facilitating simple and very efficient Gibbs sampling, as well as an Expectation Maximization algorithm for inference. Also, predicting the label vector at test time does not require doing an inference for the label embeddings and can be done in closed form. We report results on several benchmark data sets, comparing our model with various state-of-the art methods.

Tuesday December 8, 2015 19:00 - 23:59

210 C #17

210 C #17

Large-scale probabilistic predictors with and without guarantees of validity

This paper studies theoretically and empirically a method of turning machine-learning algorithms into probabilistic predictors that automatically enjoys a property of validity (perfect calibration) and is computationally efficient. The price to pay for perfect calibration is that these probabilistic predictors produce imprecise (in practice, almost precise for large data sets) probabilities. When these imprecise probabilities are merged into precise probabilities, the resulting predictors, while losing the theoretical property of perfect calibration, are consistently more accurate than the existing methods in empirical studies.

Tuesday December 8, 2015 19:00 - 23:59

210 C #49

210 C #49

LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
Consider estimating an unknown, but structured (e.g. sparse, low-rank, etc.), signal $x_0\in R^n$ from a vector $y\in R^m$ of measurements of the form $y_i=g_i(a_i^Tx_0)$, where the $a_i$'s are the rows of a known measurement matrix $A$, and, $g$ is a (potentially unknown) nonlinear and random link-function. Such measurement functions could arise in applications where the measurement device has nonlinearities and uncertainties. It could also arise by design, e.g., $g_i(x)=sign(x+z_i)$, corresponds to noisy 1-bit quantized measurements. Motivated by the classical work of Brillinger, and more recent work of Plan and Vershynin, we estimate $x_0$ via solving the Generalized-LASSO, i.e., $\hat x=\arg\min_{x}\|y-Ax_0\|_2+\lambda f(x)$ for some regularization parameter $\lambda >0$ and some (typically non-smooth) convex regularizer $f$ that promotes the structure of $x_0$, e.g. $\ell_1$-norm, nuclear-norm. While this approach seems to naively ignore the nonlinear function $g$, both Brillinger and Plan and Vershynin have shown that, when the entries of $A$ are iid standard normal, this is a good estimator of $x_0$ up to a constant of proportionality $\mu$, which only depends on $g$. In this work, we considerably strengthen these results by obtaining explicit expressions for $\|\hat x-\mu x_0\|_2$, for the regularized Generalized-LASSO, that are asymptotically precise when $m$ and $n$ grow large. A main result is that the estimation performance of the Generalized LASSO with non-linear measurements is asymptotically the same as one whose measurements are linear $y_i=\mu a_i^Tx_0+\sigma z_i$, with $\mu=E[\gamma g(\gamma)]$ and $\sigma^2=E[(g(\gamma)-\mu\gamma)^2]$, and, $\gamma$ standard normal. The derived expressions on the estimation performance are the first-known precise results in this context. One interesting consequence of our result is that the optimal quantizer of the measurements that minimizes the estimation error of the LASSO is the celebrated Lloyd-Max quantizer.

Tuesday December 8, 2015 19:00 - 23:59

210 C #82

210 C #82

Latent Bayesian melding for integrating individual and population models
In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matchingexpectations between two models, but sometimes both models are most conveniently expressed as latent variable models. We propose latent Bayesian melding, which is motivated by averaging the distributions over populations statistics of both the individual-level and the population-level models under a logarithmic opinion pool framework. In a case study on electricity disaggregation, which is a type of single-channel blind source separation problem, we show that latent Bayesian melding leads to significantly more accurate predictions than an approach based solely on generalized moment matching.

Tuesday December 8, 2015 19:00 - 23:59

210 C #25

210 C #25

Learning Bayesian Networks with Thousands of Variables

We present a method for learning Bayesian networks from data sets containingthousands of variables without the need for structure constraints. Our approachis made of two parts. The first is a novel algorithm that effectively explores thespace of possible parent sets of a node. It guides the exploration towards themost promising parent sets on the basis of an approximated score function thatis computed in constant time. The second part is an improvement of an existingordering-based algorithm for structure optimization. The new algorithm provablyachieves a higher score compared to its original formulation. On very large datasets containing up to ten thousand nodes, our novel approach consistently outper-forms the state of the art.

Tuesday December 8, 2015 19:00 - 23:59

210 C #45

210 C #45

Learning both Weights and Connections for Efficient Neural Network

Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems. Also, conventional networks fix the architecture before training starts; as a result, training cannot improve the architecture. To address these limitations, we describe a method to reduce the storage and computation required by neural networks by an order of magnitude without affecting their accuracy by learning only the important connections. Our method prunes redundant connections using a three-step method. First, we train the network to learn which connections are important. Next, we prune the unimportant connections. Finally, we retrain the network to fine tune the weights of the remaining connections. On the ImageNet dataset, our method reduced the number of parameters of AlexNet by a factor of 9×, from 61 million to 6.7 million, without incurring accuracy loss. Similar experiments with VGG-16 found that the total number of parameters can be reduced by 13×, from 138 million to 10.3 million, again with no loss of accuracy.

Tuesday December 8, 2015 19:00 - 23:59

210 C #12

210 C #12

Learning Continuous Control Policies by Stochastic Value Gradients

We present a unified framework for learning continuous control policies usingbackpropagation. It supports stochastic control by treating stochasticity in theBellman equation as a deterministic function of exogenous noise. The productis a spectrum of general policy gradient algorithms that range from model-freemethods with value functions to model-based methods without value functions.We use learned models but only require observations from the environment insteadof observations from model-predicted trajectories, minimizing the impactof compounded model errors. We apply these algorithms first to a toy stochasticcontrol problem and then to several physics-based control problems in simulation.One of these variants, SVG(1), shows the effectiveness of learning models, valuefunctions, and policies simultaneously in continuous domains.

Tuesday December 8, 2015 19:00 - 23:59

210 C #31

210 C #31

Learning Stationary Time Series using Gaussian Processes with Nonparametric Kernels
We introduce the Gaussian Process Convolution Model (GPCM), a two-stage nonparametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise process and a continuous-time linear filter drawn from Gaussian process. The GPCM is a continuous-time nonparametric-window moving average process and, conditionally, is itself a Gaussian process with a nonparametric kernel defined in a probabilistic fashion. The generative model can be equivalently considered in the frequency domain, where the power spectral density of the signal is specified using a Gaussian process. One of the main contributions of the paper is to develop a novel variational free-energy approach based on inter-domain inducing variables that efficiently learns the continuous-time linear filter and infers the driving white-noise process. In turn, this scheme provides closed-form probabilistic estimates of the covariance kernel and the noise-free signal both in denoising and prediction scenarios. Additionally, the variational inference procedure provides closed-form expressions for the approximate posterior of the spectral density given the observed data, leading to new Bayesian nonparametric approaches to spectrum estimation. The proposed GPCM is validated using synthetic and real-world signals.

Tuesday December 8, 2015 19:00 - 23:59

210 C #32

210 C #32

Learning Structured Output Representation using Deep Conditional Generative Models

Supervised deep learning has been successfully applied for many recognition problems in machine learning and computer vision. Although it can approximate a complex many-to-one function very well when large number of training data is provided, the lack of probabilistic inference of the current supervised deep learning methods makes it difficult to model a complex structured output representations. In this work, we develop a scalable deep conditional generative model for structured output variables using Gaussian latent variables. The model is trained efficiently in the framework of stochastic gradient variational Bayes, and allows a fast prediction using stochastic feed-forward inference. In addition, we provide novel strategies to build a robust structured prediction algorithms, such as recurrent prediction network architecture, input noise-injection and multi-scale prediction training methods. In experiments, we demonstrate the effectiveness of our proposed algorithm in comparison to the deterministic deep neural network counterparts in generating diverse but realistic output representations using stochastic inference. Furthermore, the proposed schemes in training methods and architecture design were complimentary, which leads to achieve strong pixel-level object segmentation and semantic labeling performance on Caltech-UCSD Birds 200 and the subset of Labeled Faces in the Wild dataset.

Tuesday December 8, 2015 19:00 - 23:59

210 C #3

210 C #3

Learning visual biases from human imagination

Although the human visual system can recognize many concepts under challengingconditions, it still has some biases. In this paper, we investigate whether wecan extract these biases and transfer them into a machine recognition system.We introduce a novel method that, inspired by well-known tools in humanpsychophysics, estimates the biases that the human visual system might use forrecognition, but in computer vision feature spaces. Our experiments aresurprising, and suggest that classifiers from the human visual system can betransferred into a machine with some success. Since these classifiers seem tocapture favorable biases in the human visual system, we further present an SVMformulation that constrains the orientation of the SVM hyperplane to agree withthe bias from human visual system. Our results suggest that transferring thishuman bias into machines may help object recognition systems generalize acrossdatasets and perform better when very little training data is available.

Tuesday December 8, 2015 19:00 - 23:59

210 C #9

210 C #9

Learning with Group Invariant Features: A Kernel Perspective.

We analyze in this paper a random feature map based on a theory of invariance (\emph{I-theory}) introduced in \cite{AnselmiLRMTP13}. More specifically, a group invariant signal signature is obtained through cumulative distributions of group-transformed random projections. Our analysis bridges invariant feature learning with kernel methods, as we show that this feature map defines an expected Haar-integration kernel that is invariant to the specified group action. We show how this non-linear random feature map approximates this group invariant kernel uniformly on a set of $N$ points. Moreover, we show that it defines a function space that is dense in the equivalent Invariant Reproducing Kernel Hilbert Space. Finally, we quantify error rates of the convergence of the empirical risk minimization, as well as the reduction in the sample complexity of a learning algorithm using such an invariant representation for signal classification, in a classical supervised learning setting

Tuesday December 8, 2015 19:00 - 23:59

210 C #38

210 C #38

Linear Response Methods for Accurate Covariance Estimates from Mean Field Variational Bayes
Mean field variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, a well known failing of MFVB is that it underestimates the uncertainty of model variables (sometimes severely) and provides no information about model variable covariance. We generalize linear response methods from statistical physics to deliver accurate uncertainty estimates for model variables---both for individual variables and coherently across variables. We call our method linear response variational Bayes (LRVB). When the MFVB posterior approximation is in the exponential family, LRVB has a simple, analytic form, even for non-conjugate models. Indeed, we make no assumptions about the form of the true posterior. We demonstrate the accuracy and scalability of our method on a range of models for both simulated and real data.

Tuesday December 8, 2015 19:00 - 23:59

210 C #39

210 C #39

Matrix Manifold Optimization for Gaussian Mixtures

We take a new look at parameter estimation for Gaussian Mixture Model (GMMs). Specifically, we advance Riemannian manifold optimization (on the manifold of positive definite matrices) as a potential replacement for Expectation Maximization (EM), which has been the de facto standard for decades. An out-of-the-box invocation of Riemannian optimization, however, fails spectacularly: it obtains the same solution as EM, but vastly slower. Building on intuition from geometric convexity, we propose a simple reformulation that has remarkable consequences: it makes Riemannian optimization not only match EM (a nontrivial result on its own, given the poor record nonlinear programming has had against EM), but also outperform it in many settings. To bring our ideas to fruition, we develop a well-tuned Riemannian LBFGS method that proves superior to known competing methods (e.g., Riemannian conjugate gradient). We hope that our results encourage a wider consideration of manifold optimization in machine learning and statistics.

Tuesday December 8, 2015 19:00 - 23:59

210 C #56

210 C #56

Measuring Sample Quality with Stein's Method
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness creates new challenges for sampler and parameter selection, since standard measures of sample quality like effective sample size do not account for asymptotic bias. To address these challenges, we introduce a new computable quality measure based on Stein's method that bounds the discrepancy between sample and target expectations over a large class of test functions. We use our tool to compare exact, biased, and deterministic sample sequences and illustrate applications to hyperparameter selection, convergence rate assessment, and quantifying bias-variance tradeoffs in posterior inference.

Tuesday December 8, 2015 19:00 - 23:59

210 C #62

210 C #62

Minimum Weight Perfect Matching via Blossom Belief Propagation
Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this paper, we develop the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds' algorithm as a sequence of LPs.

Tuesday December 8, 2015 19:00 - 23:59

210 C #80

210 C #80

Newton-Stein Method: A Second Order Method for GLMs via Stein's Lemma
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs)when the number of observations is much larger than the number of coefficients (n > > p > > 1). In this regime, optimization algorithms can immensely benefit fromapproximate second order information.We propose an alternative way of constructing the curvature information by formulatingit as an estimation problem and applying a Stein-type lemma, which allows further improvements through sub-sampling andeigenvalue thresholding.Our algorithm enjoys fast convergence rates, resembling that of second order methods, with modest per-iteration cost. We provide its convergence analysis for the case where the rows of the design matrix are i.i.d. samples with bounded support.We show that the convergence has two phases, aquadratic phase followed by a linear phase. Finally,we empirically demonstrate that our algorithm achieves the highest performancecompared to various algorithms on several datasets.

Tuesday December 8, 2015 19:00 - 23:59

210 C #73

210 C #73

On Elicitation Complexity

Elicitation is the study of statistics or properties which are computable via empirical risk minimization. While several recent papers have approached the general question of which properties are elicitable, we suggest that this is the wrong question---all properties are elicitable by first eliciting the entire distribution or data set, and thus the important question is how elicitable. Specifically, what is the minimum number of regression parameters needed to compute the property?Building on previous work, we introduce a new notion of elicitation complexity and lay the foundations for a calculus of elicitation. We establish several general results and techniques for proving upper and lower bounds on elicitation complexity. These results provide tight bounds for eliciting the Bayes risk of any loss, a large class of properties which includes spectral risk measures and several new properties of interest.

Tuesday December 8, 2015 19:00 - 23:59

210 C #98

210 C #98

On some provably correct cases of variational inference for topic models
Variational inference is an efficient, popular heuristic used in the context of latent variable models. We provide the first analysis of instances where variational inference algorithms converge to the global optimum, in the setting of topic models. Our initializations are natural, one of them being used in LDA-c, the mostpopular implementation of variational inference.In addition to providing intuition into why this heuristic might work in practice, the multiplicative, rather than additive nature of the variational inference updates forces us to usenon-standard proof arguments, which we believe might be of general theoretical interest.

Tuesday December 8, 2015 19:00 - 23:59

210 C #48

210 C #48

On the Accuracy of Self-Normalized Log-Linear Models

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as ``self-normalization'', which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that self-normalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking.We prove upper bounds on the loss in accuracy due to self-normalization, describe classes of input distributionsthat self-normalize easily, and construct explicit examples of high-variance input distributions. Our theoretical results make predictions about the difficulty of fitting self-normalized models to several classes of distributions, and we conclude with empirical validation of these predictions on both real and synthetic datasets.

Tuesday December 8, 2015 19:00 - 23:59

210 C #50

210 C #50

On the Pseudo-Dimension of Nearly Optimal Auctions
This paper develops a general approach, rooted in statistical learning theory, to learning an approximately revenue-maximizing auction from data. We introduce t-level auctions to interpolate between simple auctions, such as welfare maximization with reserve prices, and optimal auctions, thereby balancing the competing demands of expressivity and simplicity. We prove that such auctions have small representation error, in the sense that for every product distribution F over bidders’ valuations, there exists a t-level auction with small t and expected revenue close to optimal. We show that the set of t-level auctions has modest pseudo-dimension (for polynomial t) and therefore leads to small learning error. One consequence of our results is that, in arbitrary single-parameter settings, one can learn a mechanism with expected revenue arbitrarily close to optimal from a polynomial number of samples.

Tuesday December 8, 2015 19:00 - 23:59

210 C #84

210 C #84

On Variance Reduction in Stochastic Gradient Descent and its Asynchronous Variants

We study optimization algorithms based on variance reduction for stochastic gradientdescent (SGD). Remarkable recent progress has been made in this directionthrough development of algorithms like SAG, SVRG, SAGA. These algorithmshave been shown to outperform SGD, both theoretically and empirically. However,asynchronous versions of these algorithms—a crucial requirement for modernlarge-scale applications—have not been studied. We bridge this gap by presentinga unifying framework that captures many variance reduction techniques.Subsequently, we propose an asynchronous algorithm grounded in our framework,with fast convergence rates. An important consequence of our general approachis that it yields asynchronous versions of variance reduction algorithms such asSVRG, SAGA as a byproduct. Our method achieves near linear speedup in sparsesettings common to machine learning. We demonstrate the empirical performanceof our method through a concrete realization of asynchronous SVRG.

Tuesday December 8, 2015 19:00 - 23:59

210 C #77

210 C #77

Online Learning with Adversarial Delays

We study the performance of standard online learning algorithms when the feedback is delayed by an adversary. We show that \texttt{online-gradient-descent} and \texttt{follow-the-perturbed-leader} achieve regret $O(\sqrt{D})$ in the delayed setting, where $D$ is the sum of delays of each round's feedback. This bound collapses to an optimal $O(\sqrt{T})$ bound in the usual setting of no delays (where $D = T$). Our main contribution is to show that standard algorithms for online learning already have simple regret bounds in the most general setting of delayed feedback, making adjustments to the analysis and not to the algorithms themselves. Our results help affirm and clarify the success of recent algorithms in optimization and machine learning that operate in a delayed feedback model.

Tuesday December 8, 2015 19:00 - 23:59

210 C #99

210 C #99

Optimal Rates for Random Fourier Features
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show good versatility, they are computationally intensive and have poor scalability to large data as they require operations on Gram matrices. In order to mitigate this serious computational limitation, recently randomized constructions have been proposed in the literature, which allow the application of fast linear algorithms. Random Fourier features (RFF) are among the most popular and widely applied constructions: they provide an easily computable, low-dimensional feature representation for shift-invariant kernels. Despite the popularity of RFFs, very little is understood theoretically about their approximation quality. In this paper, we provide a detailed finite-sample theoretical analysis about the approximation quality of RFFs by (i) establishing optimal (in terms of the RFF dimension, and growing set size) performance guarantees in uniform norm, and (ii) presenting guarantees in L^r (1 ≤ r < ∞) norms. We also propose an RFF approximation to derivatives of a kernel with a theoretical study on its approximation quality.

Tuesday December 8, 2015 19:00 - 23:59

210 C #95

210 C #95

Parallel Correlation Clustering on Big Graphs

Given a similarity graph between items, correlation clustering (CC) groups similar items together and dissimilar ones apart. One of the most popular CC algorithms is KwikCluster: an algorithm that serially clusters neighborhoods of vertices, and obtains a 3-approximation ratio. Unfortunately, in practice KwikCluster requires a large number of clustering rounds, a potential bottleneck for large graphs.We present C4 and ClusterWild!, two algorithms for parallel correlation clustering that run in a polylogarithmic number of rounds, and provably achieve nearly linear speedups. C4 uses concurrency control to enforce serializability of a parallel clustering process, and guarantees a 3-approximation ratio. ClusterWild! is a coordination free algorithm that abandons consistency for the benefit of better scaling; this leads to a provably small loss in the 3 approximation ratio.We provide extensive experimental results for both algorithms, where we outperform the state of the art, both in terms of clustering accuracy and running time. We show that our algorithms can cluster billion-edge graphs in under 5 seconds on 32 cores, while achieving a 15x speedup.

Tuesday December 8, 2015 19:00 - 23:59

210 C #66

210 C #66

Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions

We develop \textit{parallel predictive entropy search} (PPES), a novel algorithm for Bayesian optimization of expensive black-box objective functions. At each iteration, PPES aims to select a \textit{batch} of points which will maximize the information gain about the global maximizer of the objective. Well known strategies exist for suggesting a single evaluation point based on previous observations, while far fewer are known for selecting batches of points to evaluate in parallel. The few batch selection schemes that have been studied all resort to greedy methods to compute an optimal batch. To the best of our knowledge, PPES is the first non-greedy batch Bayesian optimization strategy. We demonstrate the benefit of this approach in optimization performance on both synthetic and real world applications, including problems in machine learning, rocket science and robotics.

Tuesday December 8, 2015 19:00 - 23:59

210 C #46

210 C #46

Path-SGD: Path-Normalized Optimization in Deep Neural Networks

We revisit the choice of SGD for training deep neural networks by reconsidering the appropriate geometry in which to optimize the weights. We argue for a geometry invariant to rescaling of weights that does not affect the output of the network, and suggest Path-SGD, which is an approximate steepest descent method with respect to a path-wise regularizer related to max-norm regularization. Path-SGD is easy and efficient to implement and leads to empirical gains over SGD and AdaGrad.

Tuesday December 8, 2015 19:00 - 23:59

210 C #33

210 C #33

Planar Ultrametrics for Image Segmentation

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of finding the closest ultrametric to a specified set of distances and solve it using an LP relaxation that leverages minimum cost perfect matching as a subroutine to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentation.

Tuesday December 8, 2015 19:00 - 23:59

210 C #44

210 C #44

Policy Evaluation Using the Ω-Return

We propose the Ω-return as an alternative to the λ-return currently used by the TD(λ) family of algorithms. The benefit of the Ω-return is that it accounts for the correlation of different length returns. Because it is difficult to compute exactly, we suggest one way of approximating the Ω-return. We provide empirical studies that suggest that it is superior to the λ-return and γ-return for a variety of problems.

Tuesday December 8, 2015 19:00 - 23:59

210 C #51

210 C #51

Preconditioned Spectral Descent for Deep Learning

Deep learning presents notorious computational challenges. These challenges include, but are not limited to, the non-convexity of learning objectives and estimating the quantities needed for optimization algorithms, such as gradients. While we do not address the non-convexity, we present an optimization solution that ex- ploits the so far unused “geometry” in the objective function in order to best make use of the estimated gradients. Previous work attempted similar goals with preconditioned methods in the Euclidean space, such as L-BFGS, RMSprop, and ADA-grad. In stark contrast, our approach combines a non-Euclidean gradient method with preconditioning. We provide evidence that this combination more accurately captures the geometry of the objective function compared to prior work. We theoretically formalize our arguments and derive novel preconditioned non-Euclidean algorithms. The results are promising in both computational time and quality when applied to Restricted Boltzmann Machines, Feedforward Neural Nets, and Convolutional Neural Nets.

Tuesday December 8, 2015 19:00 - 23:59

210 C #30

210 C #30

Private Graphon Estimation for Sparse Graphs

We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph $G$, our algorithms output a node-differentially private nonparametric block model approximation. By node-differentially private, we mean that our output hides the insertion or removal of a vertex and all its adjacent edges. If $G$ is an instance of the network obtained from a generative nonparametric model defined in terms of a graphon $W$, our model guarantees consistency: as the number of vertices tends to infinity, the output of our algorithm converges to $W$ in an appropriate version of the $L_2$ norm. In particular, this means we can estimate the sizes of all multi-way cuts in $G$. Our results hold as long as $W$ is bounded, the average degree of $G$ grows at least like the log of the number of vertices, and the number of blocks goes to infinity at an appropriate rate. We give explicit error bounds in terms of the parameters of the model; in several settings, our bounds improve on or match known nonprivate results.

Tuesday December 8, 2015 19:00 - 23:59

210 C #91

210 C #91

Probabilistic Curve Learning: Coulomb Repulsion and the Electrostatic Gaussian Process

Learning of low dimensional structure in multidimensional data is a canonical problem in machine learning. One common approach is to suppose that the observed data are close to a lower-dimensional smooth manifold. There are a rich variety of manifold learning methods available, which allow mapping of data points to the manifold. However, there is a clear lack of probabilistic methods that allow learning of the manifold along with the generative distribution of the observed data. The best attempt is the Gaussian process latent variable model (GP-LVM), but identifiability issues lead to poor performance. We solve these issues by proposing a novel Coulomb repulsive process (Corp) for locations of points on the manifold, inspired by physical models of electrostatic interactions among particles. Combining this process with a GP prior for the mapping function yields a novel electrostatic GP (electroGP) process. Focusing on the simple case of a one-dimensional manifold, we develop efficient inference algorithms, and illustrate substantially improved performance in a variety of experiments including filling in missing frames in video.

Tuesday December 8, 2015 19:00 - 23:59

210 C #29

210 C #29

Probabilistic Line Searches for Stochastic Optimization
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic line search by combining the structure of existing deterministic methods with notions from Bayesian optimization. Our method retains a Gaussian process surrogate of the univariate optimization objective, and uses a probabilistic belief over the Wolfe conditions to monitor the descent. The algorithm has very low computational cost, and no user-controlled parameters. Experiments show that it effectively removes the need to define a learning rate for stochastic gradient descent.

Tuesday December 8, 2015 19:00 - 23:59

210 C #40

210 C #40

Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition
Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate than simpler sketching algorithms, yet still converges quickly for *any* matrix, independently of singular value gaps. After ~O(1/epsilon) iterations, it gives a low-rank approximation within (1+epsilon) of optimal for spectral norm error.We give the first provable runtime improvement on Simultaneous Iteration: a randomized block Krylov method, closely related to the classic Block Lanczos algorithm, gives the same guarantees in just ~O(1/sqrt(epsilon)) iterations and performs substantially better experimentally. Our analysis is the first of a Krylov subspace method that does not depend on singular value gaps, which are unreliable in practice.Furthermore, while it is a simple accuracy benchmark, even (1+epsilon) error for spectral norm low-rank approximation does not imply that an algorithm returns high quality principal components, a major issue for data applications. We address this problem for the first time by showing that both Block Krylov Iteration and Simultaneous Iteration give nearly optimal PCA for any matrix. This result further justifies their strength over non-iterative sketching methods.

Tuesday December 8, 2015 19:00 - 23:59

210 C #83

210 C #83

Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width
Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width. We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates, which have bounded hierarchy width—regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers.

Tuesday December 8, 2015 19:00 - 23:59

210 C #47

210 C #47

Reflection, Refraction, and Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics with non-smooth functions, leading to poor performance. This paper is motivated by the behavior of Hamiltonian dynamics in physical systems like optics. We introduce a modification of the Leapfrog discretization of Hamiltonian dynamics on piecewise continuous energies, where intersections of the trajectory with discontinuities are detected, and the momentum is reflected or refracted to compensate for the change in energy. We prove that this method preserves the correct stationary distribution when boundaries are affine. Experiments show that by reducing the number of rejected samples, this method improves on traditional HMC.

Tuesday December 8, 2015 19:00 - 23:59

210 C #43

210 C #43

Regularization Path of Cross-Validation Error Lower Bounds

Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances.Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be needed in cross-validation (CV) for obtaining a solution with sufficiently small CV error.In this paper we propose a novel framework for computing a lower bound of the CV errors as a function of the regularization parameter, which we call regularization path of CV error lower bounds.The proposed framework can be used for providing a theoretical approximation guarantee on a set of solutions in the sense that how far the CV error of the current best solution could be away from best possible CV error in the entire range of the regularization parameters.We demonstrate through numerical experiments that a theoretically guaranteed a choice of regularization parameter in the above sense is possible with reasonable computational costs.

Tuesday December 8, 2015 19:00 - 23:59

210 C #69

210 C #69

Sample Complexity of Episodic Fixed-Horizon Reinforcement Learning

Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for example tutoring students for exams or handling customer service requests. Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist. A natural notion of sample complexity in this setting is the number of episodes required to guarantee a certain performance with high probability (PAC guarantee). In this paper, we derive an upper PAC bound of order O(|S|²|A|H² log(1/δ)/ɛ²) and a lower PAC bound Ω(|S||A|H² log(1/(δ+c))/ɛ²) (ignoring log-terms) that match up to log-terms and an additional linear dependency on the number of states |S|. The lower bound is the first of its kind for this setting. Our upper bound leverages Bernstein's inequality to improve on previous bounds for episodic finite-horizon MDPs which have a time-horizon dependency of at least H³.

Tuesday December 8, 2015 19:00 - 23:59

210 C #90

210 C #90

Sample Complexity of Learning Mahalanobis Distance Metrics

Metric learning seeks a transformation of the feature space that enhances prediction quality for a given task. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and upper-bounds showing that sample complexity scales with the representation dimension when no assumptions are made about the underlying data distribution. In addition, by leveraging the structure of the data distribution, we provide rates fine-tuned to a specific notion of the intrinsic complexity of a given dataset, allowing us to relax the dependence on representation dimension. We show both theoretically and empirically that augmenting the metric learning optimization criterion with a simple norm-based regularization is important and can help adapt to a dataset’s intrinsic complexity yielding better generalization, thus partly explaining the empirical success of similar regularizations reported in previous works.

Tuesday December 8, 2015 19:00 - 23:59

210 C #55

210 C #55

Sampling from Probabilistic Submodular Models
Submodular and supermodular functions have found wide applicability in machine learning, capturing notions such as diversity and regularity, respectively. These notions have deep consequences for optimization, and the problem of (approximately) optimizing submodular functions has received much attention. However, beyond optimization, these notions allow specifying expressive probabilistic models that can be used to quantify predictive uncertainty via marginal inference. Prominent, well-studied special cases include Ising models and determinantal point processes, but the general class of log-submodular and log-supermodular models is much richer and little studied. In this paper, we investigate the use of Markov chain Monte Carlo sampling to perform approximate inference in general log-submodular and log-supermodular models. In particular, we consider a simple Gibbs sampling procedure, and establish two sufficient conditions, the first guaranteeing polynomial-time, and the second fast (O(nlogn)) mixing. We also evaluate the efficiency of the Gibbs sampler on three examples of such models, and compare against a recently proposed variational approach.

Tuesday December 8, 2015 19:00 - 23:59

210 C #70

210 C #70

Scale Up Nonlinear Component Analysis with Doubly Stochastic Gradients

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets. Recent attempts have employed random feature approximations to convert the problem to the primal form for linear computational complexity. However, to obtain high quality solutions, the number of random features should be the same order of magnitude as the number of data points, making such approach not directly applicable to the regime with millions of data points.We propose a simple, computationally efficient, and memory friendly algorithm based on the ``doubly stochastic gradients'' to scale up a range of kernel nonlinear component analysis, such as kernel PCA, CCA and SVD. Despite the \emph{non-convex} nature of these problems, our method enjoys theoretical guarantees that it converges at the rate $\Otil(1/t)$ to the global optimum, even for the top $k$ eigen subspace. Unlike many alternatives, our algorithm does not require explicit orthogonalization, which is infeasible on big datasets. We demonstrate the effectiveness and scalability of our algorithm on large scale synthetic and real world datasets.

Tuesday December 8, 2015 19:00 - 23:59

210 C #58

210 C #58

Semi-Proximal Mirror-Prox for Nonsmooth Composite Minimization

We propose a new first-order optimization algorithm to solve high-dimensional non-smooth composite minimization problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a non-smooth regularization penalty. The proposed algorithm, called Semi-Proximal Mirror-Prox, leverages the saddle point representation of one part of the objective while handling the other part of the objective via linear minimization over the domain. The algorithm stands in contrast with more classical proximal gradient algorithms with smoothing, which require the computation of proximal operators at each iteration and can therefore be impractical for high-dimensional problems. We establish the theoretical convergence rate of Semi-Proximal Mirror-Prox, which exhibits the optimal complexity bounds for the number of calls to linear minimization oracle. We present promising experimental results showing the interest of the approach in comparison to competing methods.

Tuesday December 8, 2015 19:00 - 23:59

210 C #87

210 C #87

SGD Algorithms based on Incomplete U-statistics: Large-Scale Minimization of Empirical Risk

In many learning problems, ranging from clustering to ranking through metric learning, empirical estimates of the risk functional consist of an average over tuples (e.g., pairs or triplets) of observations, rather than over individual observations. In this paper, we focus on how to best implement a stochastic approximation approach to solve such risk minimization problems. We argue that in the large-scale setting, gradient estimates should be obtained by sampling tuples of data points with replacement (incomplete U-statistics) instead of sampling data points without replacement (complete U-statistics based on subsamples). We develop a theoretical framework accounting for the substantial impact of this strategy on the generalization ability of the prediction model returned by the Stochastic Gradient Descent (SGD) algorithm. It reveals that the method we promote achieves a much better trade-off between statistical accuracy and computational cost. Beyond the rate bound analysis, experiments on AUC maximization and metric learning provide strong empirical evidence of the superiority of the proposed approach.

Tuesday December 8, 2015 19:00 - 23:59

210 C #75

210 C #75

Shepard Convolutional Neural Networks

Deep learning has recently been introduced to the field of low-level computer vision and image processing. Promising results have been obtained in a number of tasks including super-resolution, inpainting, deconvolution, filtering, etc. However, previously adopted neural network approaches such as convolutional neural networks and sparse auto-encoders are inherently with translation invariant operators. We found this property prevents the deep learning approaches from outperforming the state-of-the-art if the task itself requires translation variant interpolation (TVI). In this paper, we draw on Shepard interpolation and design Shepard Convolutional Neural Networks (ShCNN) which efficiently realizes end-to-end trainable TVI operators in the network. We show that by adding only a few feature maps in the new Shepard layers, the network is able to achieve stronger results than a much deeper architecture. Superior performance on both image inpainting and super-resolution is obtained where our system outperforms previous ones while keeping the running time competitive.

Tuesday December 8, 2015 19:00 - 23:59

210 C #2

210 C #2

Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
This paper is concerned with finding a solution x to a quadratic system of equations y_i = |< a_i, x >|^2, i = 1, 2, ..., m. We prove that it is possible to solve unstructured quadratic systems in n variables exactly from O(n) equations in linear time, that is, in time proportional to reading and evaluating the data. This is accomplished by a novel procedure, which starting from an initial guess given by a spectral initialization procedure, attempts to minimize a non-convex objective. The proposed algorithm distinguishes from prior approaches by regularizing the initialization and descent procedures in an adaptive fashion, which discard terms bearing too much influence on the initial estimate or search directions. These careful selection rules---which effectively serve as a variance reduction scheme---provide a tighter initial guess, more robust descent directions, and thus enhanced practical performance. Further, this procedure also achieves a near-optimal statistical accuracy in the presence of noise. Finally, we demonstrate empirically that the computational cost of our algorithm is about four times that of solving a least-squares problem of the same size.

Tuesday December 8, 2015 19:00 - 23:59

210 C #64

210 C #64

Stochastic Expectation Propagation
Expectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local-approximations that are iteratively refined for each datapoint. EP can offer analytic and computational advantages over other approximations, such as Variational Inference (VI), and is the method of choice for a number of models. The local nature of EP appears to make it an ideal candidate for performing Bayesian learning on large models in large-scale datasets settings. However, EP has a crucial limitation in this context: the number approximating factors needs to increase with the number of data-points, N, which often entails a prohibitively large memory overhead. This paper presents an extension to EP, called stochastic expectation propagation (SEP), that maintains a global posterior approximation (like VI) but updates it in a local way (like EP). Experiments on a number of canonical learning problems using synthetic and real-world datasets indicate that SEP performs almost as well as full EP, but reduces the memory consumption by a factor of N. SEP is therefore ideally suited to performing approximate Bayesian learning in the large model, large dataset setting.

Tuesday December 8, 2015 19:00 - 23:59

210 C #36

210 C #36

Structured Estimation with Atomic Norms: General Bounds and Applications

For structured estimation problems with atomic norms, recent advances in the literature express sample complexity and estimation error bounds in terms of certain geometric measures, in particular Gaussian width of the unit norm ball, Gaussian width of a spherical cap induced by a tangent cone, and a restricted norm compatibility constant. However, given an atomic norm, bounding these geometric measures can be difficult. In this paper, we present general upper bounds for such geometric measures, which only require simple information of the atomic norm under consideration, and we establish tightness of these bounds by providing the corresponding lower bounds. We show applications of our analysis to certain atomic norms, especially k-support norm, for which existing result is incomplete.

Tuesday December 8, 2015 19:00 - 23:59

210 C #100

210 C #100

SubmodBoxes: Near-Optimal Search for a Set of Diverse Object Proposals

This paper formulates the search for a set of bounding boxes (as needed in object proposal generation) as a monotone submodular maximization problem over the space of all possible bounding boxes in an image. Since the number of possible bounding boxes in an image is very large $O(#pixels^2)$, even a single linear scan to perform the greedy augmentation for submodular maximization is intractable. Thus, we formulate the greedy augmentation step as a Branch-and-Bound scheme. In order to speed up repeated application of B\&B, we propose a novel generalization of Minoux’s ‘lazy greedy’ algorithm to the B\&B tree. Theoretically, our proposed formulation provides a new understanding to the problem, and contains classic heuristic approaches such as Sliding Window+Non-Maximal Suppression (NMS) and and Efficient Subwindow Search (ESS) as special cases. Empirically, we show that our approach leads to a state-of-art performance on object proposal generation via a novel diversity measure.

Tuesday December 8, 2015 19:00 - 23:59

210 C #7

210 C #7

Submodular Hamming Metrics
We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tractable to optimize over. By exploiting submodularity, we are able to give hardness results and approximation algorithms for optimizing over such metrics. Additionally, we demonstrate empirically the effectiveness of these metrics and associated algorithms on both a metric minimization task (a form of clustering) and also a metric maximization task (generating diverse k-best lists).

Tuesday December 8, 2015 19:00 - 23:59

210 C #71

210 C #71

Subsampled Power Iteration: a Unified Algorithm for Block Models and Planted CSP's

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems (CSP), via a common generalization in terms of random bipartite graphs. Our algorithm matches up to a constant factor the best-known bounds for the number of edges (or constraints) needed for perfect recovery and its running time is linear in the number of edges used. The time complexity is significantly better than both spectral and SDP-based approaches.The main contribution of the algorithm is in the case of unequal sizes in the bipartition that arises in our reduction from the planted CSP. Here our algorithm succeeds at a significantly lower density than the spectral approaches, surpassing a barrier based on the spectral norm of a random matrix.Other significant features of the algorithm and analysis include (i) the critical use of power iteration with subsampling, which might be of independent interest; its analysis requires keeping track of multiple norms of an evolving solution (ii) the algorithm can be implemented statistically, i.e., with very limited access to the input distribution (iii) the algorithm is extremely simple to implement and runs in linear time, and thus is practical even for very large instances.

Tuesday December 8, 2015 19:00 - 23:59

210 C #101

210 C #101

Subset Selection by Pareto Optimization

Selecting the optimal subset from a large set of variables is a fundamental problem in various learning tasks such as feature selection, sparse regression, dictionary learning, etc. In this paper, we propose the POSS approach which employs evolutionary Pareto optimization to find a small-sized subset with good performance. We prove that for sparse regression, POSS is able to achieve the best-so-far theoretically guaranteed approximation performance efficiently. Particularly, for the \emph{Exponential Decay} subclass, POSS is proven to achieve an optimal solution. Empirical study verifies the theoretical results, and exhibits the superior performance of POSS to greedy and convex relaxation methods.

Tuesday December 8, 2015 19:00 - 23:59

210 C #78

210 C #78

Super-Resolution Off the Grid
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to biology to spectroscopy, where it is common to take (coarse) Fourier measurements of an object. Of particular interest is in obtaining estimation procedures which are robust to noise, with the following desirable statistical and computational properties: we seek to use coarse Fourier measurements (bounded by some \emph{cutoff frequency}); we hope to take a (quantifiably) small number of measurements; we desire our algorithm to run quickly. Suppose we have $k$ point sources in $d$ dimensions, where the points are separated by at least $\Delta$ from each other (in Euclidean distance). This work provides an algorithm with the following favorable guarantees:1. The algorithm uses Fourier measurements, whose frequencies are bounded by $O(1/\Delta)$ (up to log factors). Previous algorithms require a \emph{cutoff frequency} which may be as large as $\Omega(\sqrt{d}/\Delta)$.2. The number of measurements taken by and the computational complexity of our algorithm are bounded by a polynomial in both the number of points $k$ and the dimension $d$, with \emph{no} dependence on the separation $\Delta$. In contrast, previous algorithms depended inverse polynomially on the minimal separation and exponentially on the dimension for both of these quantities.Our estimation procedure itself is simple: we take random bandlimited measurements (as opposed to taking an exponential number of measurements on the hyper-grid). Furthermore, our analysis and algorithm are elementary (based on concentration bounds of sampling and singular value decomposition).

Tuesday December 8, 2015 19:00 - 23:59

210 C #94

210 C #94

Tensorizing Neural Networks

Deep neural networks currently demonstrate state-of-the-art performance in several domains.At the same time, models of this class are very demanding in terms of computational resources. In particular, a large amount of memory is required by commonly used fully-connected layers, making it hard to use the models on low-end devices and stopping the further increase of the model size. In this paper we convert the dense weight matrices of the fully-connected layers to the Tensor Train format such that the number of parameters is reduced by a huge factor and at the same time the expressive power of the layer is preserved.In particular, for the Very Deep VGG networks we report the compression factor of the dense weight matrix of a fully-connected layer up to 200000 times leading to the compression factor of the whole network up to 7 times.

Tuesday December 8, 2015 19:00 - 23:59

210 C #18

210 C #18

The Brain Uses Reliability of Stimulus Information when Making Perceptual Decisions

In simple perceptual decisions the brain has to identify a stimulus based on noisy sensory samples from the stimulus. Basic statistical considerations state that the reliability of the stimulus information, i.e., the amount of noise in the samples, should be taken into account when the decision is made. However, for perceptual decision making experiments it has been questioned whether the brain indeed uses the reliability for making decisions when confronted with unpredictable changes in stimulus reliability. We here show that even the basic drift diffusion model, which has frequently been used to explain experimental findings in perceptual decision making, implicitly relies on estimates of stimulus reliability. We then show that only those variants of the drift diffusion model which allow stimulus-specific reliabilities are consistent with neurophysiological findings. Our analysis suggests that the brain estimates the reliability of the stimulus on a short time scale of at most a few hundred milliseconds.

Tuesday December 8, 2015 19:00 - 23:59

210 C #20

210 C #20

The Consistency of Common Neighbors for Link Prediction in Stochastic Blockmodels

Link prediction and clustering are key problems for network-structureddata. While spectral clustering has strong theoretical guaranteesunder the popular stochastic blockmodel formulation of networks, itcan be expensive for large graphs. On the other hand, the heuristic ofpredicting links to nodes that share the most common neighbors withthe query node is much fast, and works very well in practice. We showtheoretically that the common neighbors heuristic can extract clustersw.h.p. when the graph is dense enough, and can do so even in sparsergraphs with the addition of a ``cleaning'' step. Empirical results onsimulated and real-world data support our conclusions.

Tuesday December 8, 2015 19:00 - 23:59

210 C #53

210 C #53

The Human Kernel
Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating human expertise remains elusive; for example, Gaussian processes with standard kernels struggle on function extrapolation problems that are trivial for human learners. In this paper, we create function extrapolation problems and acquire human responses, and then design a kernel learning framework to reverse engineer the inductive biases of human learners across a set of behavioral experiments. We use the learned kernels to gain psychological insights and to extrapolate in human-like ways that go beyond traditional stationary and polynomial kernels. Finally, we investigate Occam's razor in human and Gaussian process based function learning.

Tuesday December 8, 2015 19:00 - 23:59

210 C #24

210 C #24

The Population Posterior and Bayesian Modeling on Streams

Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop population variational Bayes, a new approach for using Bayesian modeling to analyze streams of data. It approximates a new type of distribution, the population posterior, which combines the notion of a population distribution of the data with Bayesian inference in a probabilistic model. We study our method with latent Dirichlet allocation and Dirichlet process mixtures on several large-scale data sets.

Tuesday December 8, 2015 19:00 - 23:59

210 C #28

210 C #28

The Self-Normalized Estimator for Counterfactual Learning
This paper identifies a severe problem of the counterfactual risk estimator typically used in batch learning from logged bandit feedback (BLBF), and proposes the use of an alternative estimator that avoids this problem.In the BLBF setting, the learner does not receive full-information feedback like in supervised learning, but observes feedback only for the actions taken by a historical policy.This makes BLBF algorithms particularly attractive for training online systems (e.g., ad placement, web search, recommendation) using their historical logs.The Counterfactual Risk Minimization (CRM) principle offers a general recipe for designing BLBF algorithms. It requires a counterfactual risk estimator, and virtually all existing works on BLBF have focused on a particular unbiased estimator.We show that this conventional estimator suffers from apropensity overfitting problem when used for learning over complex hypothesis spaces.We propose to replace the risk estimator with a self-normalized estimator, showing that it neatly avoids this problem.This naturally gives rise to a new learning algorithm -- Normalized Policy Optimizer for Exponential Models (Norm-POEM) --for structured output prediction using linear rules.We evaluate the empirical effectiveness of Norm-POEM on severalmulti-label classification problems, finding that it consistently outperforms the conventional estimator.

Tuesday December 8, 2015 19:00 - 23:59

210 C #59

210 C #59

Top-k Multiclass SVM
Class ambiguity is typical in image classification problems with a large number of classes. When classes are difficult to discriminate, it makes sense to allow k guesses and evaluate classifiers based on the top-k error instead of the standard zero-one loss. We propose top-k multiclass SVM as a direct method to optimize for top-k performance. Our generalization of the well-known multiclass SVM is based on a tight convex upper bound of the top-k error. We propose a fast optimization scheme based on an efficient projection onto the top-k simplex, which is of its own interest. Experiments on five datasets show consistent improvements in top-k accuracy compared to various baselines.

Tuesday December 8, 2015 19:00 - 23:59

210 C #61

210 C #61

Training Restricted Boltzmann Machine via the ￼Thouless-Anderson-Palmer free energy

Restricted Boltzmann machines are undirected neural networks which have been shown tobe effective in many applications, including serving as initializations fortraining deep multi-layer neural networks. One of the main reasons for their success is theexistence of efficient and practical stochastic algorithms, such as contrastive divergence,for unsupervised training. We propose an alternative deterministic iterative procedure based on an improved mean field method from statistical physics known as the Thouless-Anderson-Palmer approach. We demonstrate that our algorithm provides performance equal to, and sometimes superior to, persistent contrastive divergence, while also providing a clear and easy to evaluate objective function. We believe that this strategycan be easily generalized to other models as well as to more accurate higher-order approximations, paving the way for systematic improvements in training Boltzmann machineswith hidden units.

Tuesday December 8, 2015 19:00 - 23:59

210 C #19

210 C #19

Tree-Guided MCMC Inference for Normalized Random Measure Mixture Models

Normalized random measures (NRMs) provide a broad class of discrete random measures that are often used as priors for Bayesian nonparametric models. Dirichlet process is a well-known example of NRMs. Most of posterior inference methods for NRM mixture models rely on MCMC methods since they are easy to implement and their convergence is well studied. However, MCMC often suffers from slow convergence when the acceptance rate is low. Tree-based inference is an alternative deterministic posterior inference method, where Bayesian hierarchical clustering (BHC) or incremental Bayesian hierarchical clustering (IBHC) have been developed for DP or NRM mixture (NRMM) models, respectively. Although IBHC is a promising method for posterior inference for NRMM models due to its efficiency and applicability to online inference, its convergence is not guaranteed since it uses heuristics that simply selects the best solution after multiple trials are made. In this paper, we present a hybrid inference algorithm for NRMM models, which combines the merits of both MCMC and IBHC. Trees built by IBHC outlinespartitions of data, which guides Metropolis-Hastings procedure to employ appropriate proposals. Inheriting the nature of MCMC, our tree-guided MCMC (tgMCMC) is guaranteed to converge, and enjoys the fast convergence thanks to the effective proposals guided by trees. Experiments on both synthetic and real world datasets demonstrate the benefit of our method.

Tuesday December 8, 2015 19:00 - 23:59

210 C #42

210 C #42

Unlocking neural population non-stationarities using hierarchical dynamics models

Neural population activity often exhibits rich variability. This variability is thought to arise from single-neuron stochasticity, neural dynamics on short time-scales, as well as from modulations of neural firing properties on long time-scales, often referred to as non-stationarity. To better understand the nature of co-variability in neural circuits and their impact on cortical information processing, we introduce a hierarchical dynamics model that is able to capture inter-trial modulations in firing rates, as well as neural population dynamics. We derive an algorithm for Bayesian Laplace propagation for fast posterior inference, and demonstrate that our model provides a better account of the structure of neural firing than existing stationary dynamics models, when applied to neural population recordings from primary visual cortex.

Tuesday December 8, 2015 19:00 - 23:59

210 C #21

210 C #21

Unsupervised Learning by Program Synthesis

We introduce an unsupervised learning algorithmthat combines probabilistic modeling with solver-based techniques for program synthesis.We apply our techniques to both a visual learning domain and a language learning problem,showing that our algorithm can learn many visual concepts from only a few examplesand that it can recover some English inflectional morphology.Taken together, these results give both a new approach to unsupervised learning of symbolic compositional structures,and a technique for applying program synthesis tools to noisy data.

Tuesday December 8, 2015 19:00 - 23:59

210 C #15

210 C #15

Visalogy: Answering Visual Analogy Questions

In this paper, we study the problem of answering visual analogy questions. These questions take the form of image A is to image B as image C is to what. Answering these questions entails discovering the mapping from image A to image B and then extending the mapping to image C and searching for the image D such that the relation from A to B holds for C to D. We pose this problem as learning an embedding that encourages pairs of analogous images with similar transformations to be close together using convolutional neural networks with a quadruple Siamese architecture. We introduce a dataset of visual analogy questions in natural images, and show first results of its kind on solving analogy questions on natural images.

Tuesday December 8, 2015 19:00 - 23:59

210 C #5

210 C #5

Winner-Take-All Autoencoders

In this paper, we propose a winner-take-all method for learning hierarchical sparse representations in an unsupervised fashion. We first introduce fully-connected winner-take-all autoencoders which use mini-batch statistics to directly enforce a lifetime sparsity in the activations of the hidden units. We then propose the convolutional winner-take-all autoencoder which combines the benefits of convolutional architectures and autoencoders for learning shift-invariant sparse representations. We describe a way to train convolutional autoencoders layer by layer, where in addition to lifetime sparsity, a spatial sparsity within each feature map is achieved using winner-take-all activation functions. We will show that winner-take-all autoencoders can be used to to learn deep sparse representations from the MNIST, CIFAR-10, ImageNet, Street View House Numbers and Toronto Face datasets, and achieve competitive classification performance.

Tuesday December 8, 2015 19:00 - 23:59

210 C #11

210 C #11

Post-selection Inference for Forward Stepwise Regression, Lasso and other Adaptive Statistical procedures

Talk Slides »

In this talk I will present new inference tools for adaptive statistical procedures. These tools provide p-values and confidence intervals that have correct "post-selection" properties: they account for the selection that has already been carried out on the same data. I discuss application of these ideas to a wide variety of problems including Forward Stepwise Regression, Lasso, PCA, and graphical models. I will also discuss computational issues and software for implementation of these ideas.

This talk represents work (some joint) with many people including Jonathan Taylor, Richard Lockhart, Ryan Tibshirani, Will Fithian, Jason Lee, Dennis Sun, Yuekai Sun and Yunjin Choi.

In this talk I will present new inference tools for adaptive statistical procedures. These tools provide p-values and confidence intervals that have correct "post-selection" properties: they account for the selection that has already been carried out on the same data. I discuss application of these ideas to a wide variety of problems including Forward Stepwise Regression, Lasso, PCA, and graphical models. I will also discuss computational issues and software for implementation of these ideas.

This talk represents work (some joint) with many people including Jonathan Taylor, Richard Lockhart, Ryan Tibshirani, Will Fithian, Jason Lee, Dennis Sun, Yuekai Sun and Yunjin Choi.

Wednesday December 9, 2015 09:00 - 09:50

Level 2 room 210 AB

Level 2 room 210 AB

Learning Theory and Algorithms for Forecasting Non-stationary Time Series

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. We use our learning bounds to devise new algorithms for non-stationary time series forecasting for which we report some preliminary experimental results.

Wednesday December 9, 2015 09:50 - 10:10

Room 210 A

Room 210 A

Accelerated Mirror Descent in Continuous and Discrete Time

We study accelerated mirror descent dynamics in continuous and discrete time. Combining the original continuous-time motivation of mirror descent with a recent ODE interpretation of Nesterov's accelerated method, we propose a family of continuous-time descent dynamics for convex functions with Lipschitz gradients, such that the solution trajectories are guaranteed to converge to the optimum at a $O(1/t^2)$ rate. We then show that a large family of first-order accelerated methods can be obtained as a discretization of the ODE, and these methods converge at a $O(1/k^2)$ rate. This connection between accelerated mirror descent and the ODE provides an intuitive approach to the design and analysis of accelerated first-order algorithms.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Adaptive Online Learning

We propose a general framework for studying adaptive regret bounds in the online learning setting, subsuming model selection and data-dependent bounds. Given a data- or model-dependent bound we ask, “Does there exist some algorithm achieving this bound?” We show that modifications to recently introduced sequential complexity measures can be used to answer this question by providing sufficient conditions under which adaptive rates can be achieved. In particular each adaptive rate induces a set of so-called offset complexity measures, and obtaining small upper bounds on these quantities is sufficient to demonstrate achievability. A cornerstone of our analysis technique is the use of one-sided tail inequalities to bound suprema of offset random processes.Our framework recovers and improves a wide variety of adaptive bounds including quantile bounds, second order data-dependent bounds, and small loss bounds. In addition we derive a new type of adaptive bound for online linear optimization based on the spectral norm, as well as a new online PAC-Bayes theorem.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Bandit Smooth Convex Optimization: Improving the Bias-Variance Tradeoff

Bandit convex optimization is one of the fundamental problems in the field of online learning. The best algorithm for the general bandit convex optimization problem guarantees a regret of $\widetilde{O}(T^{5/6})$, while the best known lower bound is $\Omega(T^{1/2})$. Many attemptshave been made to bridge the huge gap between these bounds. A particularly interesting special case of this problem assumes that the loss functions are smooth. In this case, the best known algorithm guarantees a regret of $\widetilde{O}(T^{2/3})$. We present an efficient algorithm for the banditsmooth convex optimization problem that guarantees a regret of $\widetilde{O}(T^{5/8})$. Our result rules out an $\Omega(T^{2/3})$ lower bound and takes a significant step towards the resolution of this open problem.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Empirical Localization of Homogeneous Divergences on Discrete Sample Spaces

In this paper, we propose a novel parameter estimator for probabilistic models on discrete space. The proposed estimator is derived from minimization of homogeneous divergence and can be constructed without calculation of the normalization constant, which is frequently infeasible for models in the discrete space. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality, and reveal a relationship with the alpha-divergence. Small experiments show that the proposed estimator attains comparable performance to the MLE with drastically lower computational cost.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Information-theoretic lower bounds for convex optimization with erroneous oracles

We consider the problem of optimizing convex and concave functions with access to an erroneous zeroth-order oracle. In particular, for a given function $x \to f(x)$ we consider optimization when one is given access to absolute error oracles that return values in [f(x) - \epsilon,f(x)+\epsilon] or relative error oracles that return value in [(1+\epsilon)f(x), (1 +\epsilon)f (x)], for some \epsilon larger than 0. We show stark information theoretic impossibility results for minimizing convex functions and maximizing concave functions over polytopes in this model.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Market Scoring Rules Act As Opinion Pools For Risk-Averse Agents

A market scoring rule (MSR) – a popular tool for designing algorithmic prediction markets – is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent’s risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents’ true probabilities. In particular, the logarithmic market scoring rule acts as a logarithmic pool for constant absolute risk aversion utility agents, and as a linear pool for an atypical budget-constrained agent utility with decreasing absolute risk aversion. We also point out the interpretation of a market maker under these conditions as a Bayesian learner even when agent beliefs are static.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Multi-Layer Feature Reduction for Tree Structured Group Lasso via Hierarchical Projection

Tree structured group Lasso (TGL) is a powerful technique in uncovering the tree structured sparsity over the features, where each node encodes a group of features. It has been applied successfully in many real-world applications. However, with extremely large feature dimensions, solving TGL remains a significant challenge due to its highly complicated regularizer. In this paper, we propose a novel Multi-Layer Feature reduction method (MLFre) to quickly identify the inactive nodes (the groups of features with zero coefficients in the solution) hierarchically in a top-down fashion, which are guaranteed to be irrelevant to the response. Thus, we can remove the detected nodes from the optimization without sacrificing accuracy. The major challenge in developing such testing rules is due to the overlaps between the parents and their children nodes. By a novel hierarchical projection algorithm, MLFre is able to test the nodes independently from any of their ancestor nodes. Moreover, we can integrate MLFre---that has a low computational cost---with any existing solvers. Experiments on both synthetic and real data sets demonstrate that the speedup gained by MLFre can be orders of magnitude.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Optimal Testing for Properties of Distributions

Given samples from an unknown distribution, p, is it possible to distinguish whether p belongs to some class of distributions C versus p being far from every distribution in C? This fundamental question has receivedtremendous attention in Statistics, albeit focusing onasymptotic analysis, as well as in Computer Science, wherethe emphasis has been on small sample size and computationalcomplexity. Nevertheless, even for basic classes ofdistributions such as monotone, log-concave, unimodal, and monotone hazard rate, the optimal sample complexity is unknown.We provide a general approach via which we obtain sample-optimal and computationally efficient testers for all these distribution families. At the core of our approach is an algorithm which solves the following problem:Given samplesfrom an unknown distribution p, and a known distribution q, are p and q close in Chi^2-distance, or far in total variation distance?The optimality of all testers is established by providing matching lower bounds. Finally, a necessary building block for our tester and important byproduct of our work are the first known computationally efficient proper learners for discretelog-concave and monotone hazard rate distributions. We exhibit the efficacy of our testers via experimental analysis.

Wednesday December 9, 2015 10:10 - 10:35

Room 210 A

Room 210 A

Deep Visual Analogy-Making

In addition to identifying the content within a single image, relating images and generating related images are critical tasks for image understanding. Recently, deep convolutional networks have yielded breakthroughs in producing image labels, annotations and captions, but have only just begun to be used for producing high-quality image outputs. In this paper we develop a novel deep network trained end-to-end to perform visual analogy making, which is the task of transforming a query image according to an example pair of related images. Solving this problem requires both accurately recognizing a visual relationship and generating a transformed query image accordingly. Inspired by recent advances in language modeling, we propose to solve visual analogies by learning to map images to a neural embedding in which analogical reasoning is simple, such as by vector subtraction and addition. In experiments, our model effectively models visual analogies on several datasets: 2D shapes, animated video game sprites, and 3D car models.

Wednesday December 9, 2015 10:55 - 11:35

Room 210 A

Room 210 A

End-To-End Memory Networks

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

Wednesday December 9, 2015 10:55 - 11:35

Room 210 A

Room 210 A

Attention-Based Models for Speech Recognition

Recurrent sequence generators conditioned on input data through an attention mechanism have recently shown very good performance on a range of tasks including machine translation, handwriting synthesis and image caption generation. We extend the attention-mechanism with features needed for speech recognition. We show that while an adaptation of the model used for machine translation reaches a competitive 18.6\% phoneme error rate (PER) on the TIMIT phoneme recognition task, it can only be applied to utterances which are roughly as long as the ones it was trained on. We offer a qualitative explanation of this failure and propose a novel and generic method of adding location-awareness to the attention mechanism to alleviate this issue. The new method yields a model that is robust to long inputs and achieves 18\% PER in single utterances and 20\% in 10-times longer (repeated) utterances. Finally, we propose a change to the attention mechanism that prevents it from concentrating too much on single frames, which further reduces PER to 17.6\% level.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Deep Convolutional Inverse Graphics Network

This paper presents the Deep Convolution Inverse Graphics Network (DC-IGN), a model that aims to learn an interpretable representation of images, disentangled with respect to three-dimensional scene structure and viewing transformations such as depth rotations and lighting variations. The DC-IGN model is composed of multiple layers of convolution and de-convolution operators and is trained using the Stochastic Gradient Variational Bayes (SGVB) algorithm. We propose a training procedure to encourage neurons in the graphics code layer to represent a specific transformation (e.g. pose or light). Given a single input image, our model can generate new images of the same object with variations in pose and lighting. We present qualitative and quantitative tests of the model's efficacy at learning a 3D rendering engine for varied object classes including faces and chairs.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Learning to Segment Object Candidates

Recent object detection systems rely on two critical steps: (1) a set of object proposals is predicted as efficiently as possible, and (2) this set of candidate proposals is then passed to an object classifier. Such approaches have been shown they can be fast, while achieving the state of the art in detection performance. In this paper, we propose a new way to generate object proposals, introducing an approach based on a discriminative convolutional network. Our model is trained jointly with two objectives: given an image patch, the first part of the system outputs a class-agnostic segmentation mask, while the second part of the system outputs the likelihood of the patch being centered on a full object. At test time, the model is efficiently applied on the whole test image and generates a set of segmentation masks, each of them being assigned with a corresponding object likelihood score. We show that our model yields significant improvements over state-of-the-art object proposal algorithms. In particular, compared to previous approaches, our model obtains substantially higher object recall using fewer proposals. We also show that our model is able to generalize to unseen categories it has not seen during training. Unlike all previous approaches for generating object masks, we do not rely on edges, superpixels, or any other form of low-level segmentation.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Semi-supervised Convolutional Neural Networks for Text Categorization via Region Embedding

This paper presents a new semi-supervised framework with convolutional neural networks (CNNs) for text categorization. Unlike the previous approaches that rely on word embeddings, our method learns embeddings of small text regions from unlabeled data for integration into a supervised CNN. The proposed scheme for embedding learning is based on the idea of two-view semi-supervised learning, which is intended to be useful for the task of interest even though the training is done on unlabeled data. Our models achieve better results than previous approaches on sentiment classification and topic classification tasks.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Spatial Transformer Networks

Convolutional Neural Networks define an exceptionallypowerful class of model, but are still limited by the lack of abilityto be spatially invariant to the input data in a computationally and parameterefficient manner. In this work we introduce a new learnable module, theSpatial Transformer, which explicitly allows the spatial manipulation ofdata within the network. This differentiable module can be insertedinto existing convolutional architectures, giving neural networks the ability toactively spatially transform feature maps, conditional on the feature map itself,without any extra training supervision or modification to the optimisation process. We show that the useof spatial transformers results in models which learn invariance to translation,scale, rotation and more generic warping, resulting in state-of-the-artperformance on several benchmarks, and for a numberof classes of transformations.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

The Return of the Gating Network: Combining Generative Models and Discriminative Training in Natural Image Priors

In recent years, approaches based on machine learning have achieved state-of-the-art performance on image restoration problems. Successful approaches include both generative models of natural images as well as discriminative training of deep neural networks. Discriminative training of feed forward architectures allows explicit control over the computational cost of performing restoration and therefore often leads to better performance at the same cost at run time. In contrast, generative models have the advantage that they can be trained once and then adapted to any image restoration task by a simple use of Bayes' rule. In this paper we show how to combine the strengths of both approaches by training a discriminative, feed-forward architecture to predict the state of latent variables in a generative model of natural images. We apply this idea to the very successful Gaussian Mixture Model (GMM) of natural images. We show that it is possible to achieve comparable performance as the original GMM but with two orders of magnitude improvement in run time while maintaining the advantage of generative models.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Training Very Deep Networks

Theoretical and empirical evidence indicates that the depth of neural networks is crucial for their success. However, training becomes more difficult as depth increases, and training of very deep networks remains an open problem. Here we introduce a new architecture designed to overcome this. Our so-called highway networks allow unimpeded information flow across many layers on information highways. They are inspired by Long Short-Term Memory recurrent networks and use adaptive gating units to regulate the information flow. Even with hundreds of layers, highway networks can be trained directly through simple gradient descent. This enables the study of extremely deep and efficient architectures.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Where are they looking?

Humans have the remarkable ability to follow the gaze of other people to identify what they are looking at. Following eye gaze, or gaze-following, is an important ability that allows us to understand what other people are thinking, the actions they are performing, and even predict what they might do next. Despite the importance of this topic, this problem has only been studied in limited scenarios within the computer vision community. In this paper, we propose a deep neural network-based approach for gaze-following and a new benchmark dataset for thorough evaluation. Given an image and the location of a head, our approach follows the gaze of the person and identifies the object being looked at. After training, the network is able to discover how to extract head pose and gaze orientation, and to select objects in the scene that are in the predicted line of sight and likely to be looked at (such as televisions, balls and food). The quantitative evaluation shows that our approach produces reliable results, even when viewing only the back of the head. While our method outperforms several baseline approaches, we are still far from reaching human performance at this task. Overall, we believe that this is a challenging and important task that deserves more attention from the community.

Wednesday December 9, 2015 11:35 - 12:00

Room 210 A

Room 210 A

Diagnosis and Therapy of Psychiatric Disorders Based on Brain Dynamics

Arthur Winfree was one of the pioneers who postulated that several diseases are actually disorders of dynamics of biological systems. Following this path, many now believe that psychiatric diseases are disorders of brain dynamics. Combination of noninvasive brain measurement techniques, brain decoding and neurofeedback, and machine learning algorithms opened up a revolutionary pathway to quantitative diagnosis and therapy of neuropsychiatric disorders.

Wednesday December 9, 2015 14:00 - 14:50

Level 2 room 210 AB

Level 2 room 210 AB

A Reduced-Dimension fMRI Shared Response Model

Multi-subject fMRI data is critical for evaluating the generality and validity of findings across subjects, and its effective utilization helps improve analysis sensitivity. We develop a shared response model for aggregating multi-subject fMRI data that accounts for different functional topographies among anatomically aligned datasets. Our model demonstrates improved sensitivity in identifying a shared response for a variety of datasets and anatomical brain regions of interest. Furthermore, by removing the identified shared response, it allows improved detection of group differences. The ability to identify what is shared and what is not shared opens the model to a wide range of multi-subject fMRI studies.

Wednesday December 9, 2015 14:50 - 15:30

Room 210 A

Room 210 A

Attractor Network Dynamics Enable Preplay and Rapid Path Planning in Maze–like Environments

Rodents navigating in a well-known environment can rapidly learn and revisit observed reward locations, often after a single trial. While the mechanism for rapid path planning is unknown, the CA3 region in the hippocampus plays an important role, and emerging evidence suggests that place cell activity during hippocampal "preplay" periods may trace out future goal-directed trajectories. Here, we show how a particular mapping of space allows for the immediate generation of trajectories between arbitrary start and goal locations in an environment, based only on the mapped representation of the goal. We show that this representation can be implemented in a neural attractor network model, resulting in bump--like activity profiles resembling those of the CA3 region of hippocampus. Neurons tend to locally excite neurons with similar place field centers, while inhibiting other neurons with distant place field centers, such that stable bumps of activity can form at arbitrary locations in the environment. The network is initialized to represent a point in the environment, then weakly stimulated with an input corresponding to an arbitrary goal location. We show that the resulting activity can be interpreted as a gradient ascent on the value function induced by a reward at the goal location. Indeed, in networks with large place fields, we show that the network properties cause the bump to move smoothly from its initial location to the goal, around obstacles or walls. Our results illustrate that an attractor network with hippocampal-like attributes may be important for rapid path planning.

Wednesday December 9, 2015 14:50 - 15:30

Room 210 A

Room 210 A

A Tractable Approximation to Optimal Point Process Filtering: Application to Neural Encoding

The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal encoding/decoding strategies, which are of significant relevance to Computational Neuroscience. We develop an analytically tractable Bayesian approximation to optimal filtering based on point process observations, which allows us to introduce distributional assumptions about sensory cell properties, that greatly facilitates the analysis of optimal encoding in situations deviating from common assumptions of uniform coding. The analytic framework leads to insights which are difficult to obtain from numerical algorithms, and is consistent with experiments about the distribution of tuning curve centers. Interestingly, we find that the information gained from the absence of spikes may be crucial to performance.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Action-Conditional Video Prediction using Deep Networks in Atari Games

Motivated by vision-based reinforcement learning (RL) problems, in particular Atari games from the recent benchmark Aracade Learning Environment (ALE), we consider spatio-temporal prediction problems where future (image-)frames are dependent on control variables or actions as well as previous frames. While not composed of natural scenes, frames in Atari games are high-dimensional in size, can involve tens of objects with one or more objects being controlled by the actions directly and many other objects being influenced indirectly, can involve entry and departure of objects, and can involve deep partial observability. We propose and evaluate two deep neural network architectures that consist of encoding, action-conditional transformation, and decoding layers based on convolutional neural networks and recurrent neural networks. Experimental results show that the proposed architectures are able to generate visually-realistic frames that are also useful for control over approximately 100-step action-conditional futures in some games. To the best of our knowledge, this paper is the first to make and evaluate long-term predictions on high-dimensional video conditioned by control inputs.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Backpropagation for Energy-Efficient Neuromorphic Computing

Solving real world problems with embedded neural networks requires both training algorithms that achieve high performance and compatible hardware that runs in real time while remaining energy efficient. For the former, deep learning using backpropagation has recently achieved a string of successes across many domains and datasets. For the latter, neuromorphic chips that run spiking neural networks have recently achieved unprecedented energy efficiency. To bring these two advances together, we must first resolve the incompatibility between backpropagation, which uses continuous-output neurons and synaptic weights, and neuromorphic designs, which employ spiking neurons and discrete synapses. Our approach is to treat spikes and discrete synapses as continuous probabilities, which allows training the network using standard backpropagation. The trained network naturally maps to neuromorphic hardware by sampling the probabilities to create one or more networks, which are merged using ensemble averaging. To demonstrate, we trained a sparsely connected network that runs on the TrueNorth chip using the MNIST dataset. With a high performance network (ensemble of $64$), we achieve $99.42\%$ accuracy at $121 \mu$J per image, and with a high efficiency network (ensemble of $1$) we achieve $92.7\%$ accuracy at $0.408 \mu$J per image.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Color Constancy by Learning to Predict Chromaticity from Luminance

Color constancy is the recovery of true surface color from observed color, and requires estimating the chromaticity of scene illumination to correct for the bias it induces. In this paper, we show that the per-pixel color statistics of natural scenes---without any spatial or semantic context---can by themselves be a powerful cue for color constancy. Specifically, we describe an illuminant estimation method that is built around a "classifier" for identifying the true chromaticity of a pixel given its luminance (absolute brightness across color channels). During inference, each pixel's observed color restricts its true chromaticity to those values that can be explained by one of a candidate set of illuminants, and applying the classifier over these values yields a distribution over the corresponding illuminants. A global estimate for the scene illuminant is computed through a simple aggregation of these distributions across all pixels. We begin by simply defining the luminance-to-chromaticity classifier by computing empirical histograms over discretized chromaticity and luminance values from a training set of natural images. These histograms reflect a preference for hues corresponding to smooth reflectance functions, and for achromatic colors in brighter pixels. Despite its simplicity, the resulting estimation algorithm outperforms current state-of-the-art color constancy methods. Next, we propose a method to learn the luminance-to-chromaticity classifier "end-to-end". Using stochastic gradient descent, we set chromaticity-luminance likelihoods to minimize errors in the final scene illuminant estimates on a training set. This leads to further improvements in accuracy, most significantly in the tail of the error distribution.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Decoupled Deep Neural Network for Semi-supervised Semantic Segmentation

We propose a novel deep neural network architecture for semi-supervised semantic segmentation using heterogeneous annotations. Contrary to existing approaches posing semantic segmentation as region-based classification, our algorithm decouples classification and segmentation, and learns a separate network for each task. In this architecture, labels associated with an image are identified by classification network, and binary segmentation is subsequently performed for each identified label by segmentation network. The decoupled architecture enables us to learn classification and segmentation networks separately based on the training data with image-level and pixel-wise class labels, respectively. It facilitates to reduce search space for segmentation effectively by exploiting class-specific activation maps obtained from bridging layers. Our algorithm shows outstanding performance compared to other semi-supervised approaches even with much less training images with strong annotations in PASCAL VOC dataset.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Inferring Algorithmic Patterns with Stack-Augmented Recurrent Nets

Despite the recent achievements in machine learning, we are still very far from achieving real artificial intelligence. In this paper, we discuss the limitations of standard deep learning approaches and show that some of these limitations can be overcome by learning how to grow the complexity of a model in a structured way. Specifically, we study the simplest sequence prediction problems that are beyond the scope of what is learnable with standard recurrent networks, algorithmically generated sequences which can only be learned by models which have the capacity to count and to memorize sequences. We show that some basic algorithms can be learned from sequential data using a recurrent network associated with a trainable memory.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Learning Wake-Sleep Recurrent Attention Models

Despite their success, convolutional neural networks are computationally expensive because they must examine all image locations. Stochastic attention-based models have been shown to improve computational efficiency at test time, but they remain difficult to train because of intractable posterior inference and high variance in the stochastic gradient estimates. Borrowing techniques from the literature on training deep generative models, we present the Wake-Sleep Recurrent Attention Model, a method for training stochastic attention networks which improves posterior inference and which reduces the variability in the stochastic gradients. We show that our method can greatly speed up the training time for stochastic attention networks in the domains of image classification and caption generation.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

On-the-Job Learning with Bayesian Decision Theory

Our goal is to deploy a high-accuracy system starting with zero training examples. We consider an “on-the-job” setting, where as inputs arrive, we use real-time crowdsourcing to resolve uncertainty where needed and output our prediction when confident. As the model improves over time, the reliance on crowdsourcing queries decreases. We cast our setting as a stochastic game based on Bayesian decision theory, which allows us to balance latency, cost, and accuracy objectives in a principled way. Computing the optimal policy is intractable, so we develop an approximation based on Monte Carlo Tree Search. We tested our approach on three datasets-- named-entity recognition, sentiment classification, and image classification. On the NER task we obtained more than an order of magnitude reduction in cost compared to full human annotation, while boosting performance relative to the expert provided labels. We also achieve a 8% F1 improvement over having a single human label the whole set, and a 28% F1 improvement over online learning.

Wednesday December 9, 2015 15:30 - 16:00

Room 210 A

Room 210 A

Computational Principles for Deep Neuronal Architectures

Recent progress in machine applications of deep neural networks have highlighted the need for a theoretical understanding of the capacity and limitations of these architectures. I will review our understanding of sensory processing in such architectures in the context of the hierarchies of processing stages observed in many brain systems. I will also address the possible roles of recurrent and top - down connections, which are prominent features of brain information processing circuits.

Wednesday December 9, 2015 16:30 - 17:20

Level 2 room 210 AB

Level 2 room 210 AB

Efficient Exact Gradient Update for training Deep Networks with Very Large Sparse Targets

An important class of problems involves training deep neural networks with sparse prediction targets of very high dimension D. These occur naturally in e.g. neural language models or the learning of word-embeddings, often posed as predicting the probability of next words among a vocabulary of size D (e.g. 200,000). Computing the equally large, but typically non-sparse D-dimensional output vector from a last hidden layer of reasonable dimension d (e.g. 500) incurs a prohibitive $O(Dd)$ computational cost for each example, as does updating the $D \times d$ output weight matrix and computing the gradient needed for backpropagation to previous layers. While efficient handling of large sparse network inputs is trivial, this case of large sparse targets is not, and has thus so far been sidestepped with approximate alternatives such as hierarchical softmax or sampling-based approximations during training. In this work we develop an original algorithmic approach that, for a family of loss functions that includes squared error and spherical softmax, can compute the exact loss, gradient update for the output weights, and gradient for backpropagation, all in $O(d^2)$ per example instead of $O(Dd)$, remarkably without ever computing the D-dimensional output. The proposed algorithm yields a speedup of $\frac{D}{4d}$, i.e. two orders of magnitude for typical sizes, for that critical part of the computations that often dominates the training time in this kind of network architecture.

Wednesday December 9, 2015 17:20 - 17:40

Room 210 A

Room 210 A

Equilibrated adaptive learning rates for non-convex optimization

Parameter-specific adaptive learning rate methods are computationally efficient ways to reduce the ill-conditioning problems encountered when training large deep networks. Following recent work that strongly suggests that most of thecritical points encountered when training such networks are saddle points, we find how considering the presence of negative eigenvalues of the Hessian could help us design better suited adaptive learning rate schemes. We show that the popular Jacobi preconditioner has undesirable behavior in the presence of both positive and negative curvature, and present theoretical and empirical evidence that the so-called equilibration preconditioner is comparatively better suited to non-convex problems. We introduce a novel adaptive learning rate scheme, called ESGD, based on the equilibration preconditioner. Our experiments demonstrate that both schemes yield very similar step directions but that ESGD sometimes surpasses RMSProp in terms of convergence speed, always clearly improving over plain stochastic gradient descent.

Wednesday December 9, 2015 17:40 - 18:00

Room 210 A

Room 210 A

NEXT: A System for Real-World Development, Evaluation, and Application of Active Learning

Active learning methods automatically adapt data collection by selecting the most informative samples in order to accelerate machine learning. Because of this, real-world testing and comparing active learning algorithms requires collecting new datasets (adaptively), rather than simply applying algorithms to benchmark datasets, as is the norm in (passive) machine learning research. To facilitate the development, testing and deployment of active learning for real applications, we have built an open-source software system for large-scale active learning research and experimentation. The system, called NEXT, provides a unique platform for real-world, reproducible active learning research. This paper details the challenges of building the system and demonstrates its capabilities with several experiments. The results show how experimentation can help expose strengths and weaknesses of active learning algorithms, in sometimes unexpected and enlightening ways.

Wednesday December 9, 2015 17:40 - 18:00

Room 210 A

Room 210 A

Pointer Networks

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that arediscrete tokens corresponding to positions in an input sequence.Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines,because the number of target classes in eachstep of the output depends on the length of the input, which is variable.Problems such as sorting variable sized sequences, and various combinatorialoptimization problems belong to this class. Our model solvesthe problem of variable size output dictionaries using a recently proposedmechanism of neural attention. It differs from the previous attentionattempts in that, instead of using attention to blend hidden units of anencoder to a context vector at each decoder step, it uses attention asa pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net).We show Ptr-Nets can be used to learn approximate solutions to threechallenging geometric problems -- finding planar convex hulls, computingDelaunay triangulations, and the planar Travelling Salesman Problem-- using training examples alone. Ptr-Nets not only improve oversequence-to-sequence with input attention, butalso allow us to generalize to variable size output dictionaries.We show that the learnt models generalize beyond the maximum lengthsthey were trained on. We hope our results on these taskswill encourage a broader exploration of neural learning for discreteproblems.

Wednesday December 9, 2015 17:40 - 18:00

Room 210 A

Room 210 A

Precision-Recall-Gain Curves: PR Analysis Done Right

Precision-Recall analysis abounds in applications of binary classification where true negatives do not add value and hence should not affect assessment of the classifier's performance. Perhaps inspired by the many advantages of receiver operating characteristic (ROC) curves and the area under such curves for accuracy-based performance assessment, many researchers have taken to report Precision-Recall (PR) curves and associated areas as performance metric. We demonstrate in this paper that this practice is fraught with difficulties, mainly because of incoherent scale assumptions -- e.g., the area under a PR curve takes the arithmetic mean of precision values whereas the $F_{\beta}$ score applies the harmonic mean. We show how to fix this by plotting PR curves in a different coordinate system, and demonstrate that the new Precision-Recall-Gain curves inherit all key advantages of ROC curves. In particular, the area under Precision-Recall-Gain curves conveys an expected $F_1$ score on a harmonic scale, and the convex hull of a Precision-Recall-Gain curve allows us to calibrate the classifier's scores so as to determine, for each operating point on the convex hull, the interval of $\beta$ values for which the point optimises $F_{\beta}$. We demonstrate experimentally that the area under traditional PR curves can easily favour models with lower expected $F_1$ score than others, and so the use of Precision-Recall-Gain curves will result in better model selection.

Wednesday December 9, 2015 17:40 - 18:00

Room 210 A

Room 210 A

Structured Transforms for Small-Footprint Deep Learning

We consider the task of building compact deep learning pipelines suitable for deploymenton storage and power constrained mobile devices. We propose a uni-fied framework to learn a broad family of structured parameter matrices that arecharacterized by the notion of low displacement rank. Our structured transformsadmit fast function and gradient evaluation, and span a rich range of parametersharing configurations whose statistical modeling capacity can be explicitly tunedalong a continuum from structured to unstructured. Experimental results showthat these transforms can significantly accelerate inference and forward/backwardpasses during training, and offer superior accuracy-compactness-speed tradeoffsin comparison to a number of existing techniques. In keyword spotting applicationsin mobile speech recognition, our methods are much more effective thanstandard linear low-rank bottleneck layers and nearly retain the performance ofstate of the art models, while providing more than 3.5-fold compression.

Wednesday December 9, 2015 17:40 - 18:00

Room 210 A

Room 210 A

Accelerated Deep Learning on GPUs: From Large Scale Training to Embedded Deployment

Time is critical when developing and training the the right network on real-world datasets. GPUs offer a great computational advantage for training deep networks. Newly developed hardware resources, such as the DIGITS DevBox, can greatly reduce this development time.

Using multiple GPUs at the same time allows both multi-GPU training and parallel network model tuning to accelerate training. The four Titan X GPUs in the DIGITS DevBox allow rapid development in a single deskside appliance. Libraries are key to maximizing performance when exploiting the power of the GPU. CUDA libraries, including the NVIDIA cuDNN deep learning library, are also used to accelerate training. cuDNN is an optimized library comprised of functions commonly used to create artificial neural networks. This library includes activation functions, convolutions, and Fourier transforms, with calls catered to processing neural network data. This library is designed with deep neural network frameworks in mind and is easily used with popular open source frameworks such as Torch, Caffe, and Theano.

A trained deep neural network learns its features through an iterative process, convolving abstracted features to discern between the objects it has been trained to identify. NVIDIA DIGITS allows researchers to quickly and easily visualize the layers of trained networks. This novel visualization tool can be used with any GPU accelerated platform and works with popular frameworks like Caffe and Torch. Working with popular frameworks enables easy deployment of trained networks to other platforms, such as embedded platforms. This demonstration will show how easy it is to quickly develop a trained network using multiple GPUs on the DIGITS DevBox with the DIGITS software and deploy it to the newly released embedded platform for classification on a mobile deployment scenario.

Using multiple GPUs at the same time allows both multi-GPU training and parallel network model tuning to accelerate training. The four Titan X GPUs in the DIGITS DevBox allow rapid development in a single deskside appliance. Libraries are key to maximizing performance when exploiting the power of the GPU. CUDA libraries, including the NVIDIA cuDNN deep learning library, are also used to accelerate training. cuDNN is an optimized library comprised of functions commonly used to create artificial neural networks. This library includes activation functions, convolutions, and Fourier transforms, with calls catered to processing neural network data. This library is designed with deep neural network frameworks in mind and is easily used with popular open source frameworks such as Torch, Caffe, and Theano.

A trained deep neural network learns its features through an iterative process, convolving abstracted features to discern between the objects it has been trained to identify. NVIDIA DIGITS allows researchers to quickly and easily visualize the layers of trained networks. This novel visualization tool can be used with any GPU accelerated platform and works with popular frameworks like Caffe and Torch. Working with popular frameworks enables easy deployment of trained networks to other platforms, such as embedded platforms. This demonstration will show how easy it is to quickly develop a trained network using multiple GPUs on the DIGITS DevBox with the DIGITS software and deploy it to the newly released embedded platform for classification on a mobile deployment scenario.

Wednesday December 9, 2015 19:00 - 23:55

210D

210D

CodaLab Worksheets for Reproducible, Executable Papers

We are interested in solving two infrastructural problems in data-centric fields such as machine learning: First, an inordinate amount of time is spent on preprocessing datasets, getting other people's code to run, writing evaluation/visualization scripts, with much of this effort duplicated across different research groups. Second, a only static set of final results are ever published, leaving it up to the reader to guess how the various methods would fare in unreported scenarios. We present CodaLab Worksheets, a new platform which aims to tackle these two problems by creating an online community around sharing and executing immutable components called bundles, thereby streamlining the research process.

Wednesday December 9, 2015 19:00 - 23:55

210D

210D

Data-Driven Speech Animation

Speech animation is an extremely tedious task, where the animation artist must manually animate the face to match the spoken audio. The often prohibitive cost of speech animation has limited the types of animations that are feasible, including localization to different languages.

In this demo, we will showcase a new machine learning approach for automated speech animation. Given audio or phonetic input, our approach predicts the lower-face configurations of an animated character to match the input. In our demo, you can speak to our system, and our system will automatically animate an animated character to lip sync to your speech.

The technical details can be found in a recent KDD paper titled "A Decision Tree Framework for Spatiotemporal Sequence Prediction" by Taehwan Kim, Yisong Yue, Sarah Taylor, and Iain Matthews.

In this demo, we will showcase a new machine learning approach for automated speech animation. Given audio or phonetic input, our approach predicts the lower-face configurations of an animated character to match the input. In our demo, you can speak to our system, and our system will automatically animate an animated character to lip sync to your speech.

The technical details can be found in a recent KDD paper titled "A Decision Tree Framework for Spatiotemporal Sequence Prediction" by Taehwan Kim, Yisong Yue, Sarah Taylor, and Iain Matthews.

Wednesday December 9, 2015 19:00 - 23:55

210D

210D

Interactive Incremental Question Answering

We present a machine learning system that plays a trivia game called "quiz bowl", in which questions are incrementally revealed to players. This task requires players (both human and computer) to decide not only what answer to guess but also when to interrupt the moderator ("buzz in") with that guess. Our system uses a recently-introduced deep learning model called the deep averaging network (or DAN) to generate a set of candidate guesses given a partially-revealed question. For each candidate guess, features are generated from language models and fed to a classifier that decides whether to buzz in with that guess. Previous demonstrations have shown that our system can compete with skilled human players.

http://cs.umd.edu/~miyyer/qblearn/index.html

http://cs.umd.edu/~miyyer/qblearn/index.html

Wednesday December 9, 2015 19:00 - 23:55

210D

210D

Scaling up visual search for product recommendation

We demonstrate that, with the availability of distributed computation platforms such as Amazon Web Services and open-source tools such as Caffe, it is possible for a small engineering team to build, launch and maintain a cost-effective, large-scale visual search system. This demo showcases an interactive visual search system with more than 1 billion Pinterest image in its index built by a team of 2 engineers. By sharing our implementation details and learnings from launching a commercial visual search engine from scratch, we hope visual search becomes more widely incorporated into today’s commercial applications.

Wednesday December 9, 2015 19:00 - 23:55

210D

210D

The pMMF multiresolution matrix factorization library

pMMF is a high performance, general purpose, parallel C++ library for computing Multiresolution Matrix Factorizations at massive scales. In addition to its C++ API, pMMF can also be accessed from Matlab or through the command line. We demonstrate pMMF with an interactive visualization, showing what it does to graphs/networks.

http://people.cs.uchicago.edu/~risi/MMF/index.html

http://people.cs.uchicago.edu/~risi/MMF/index.html

Wednesday December 9, 2015 19:00 - 23:55

210D

210D

A Complete Recipe for Stochastic Gradient MCMC

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic simulations. However, such stochastic gradient MCMC samplers have lagged behind their full-data counterparts in terms of the complexity of dynamics considered since proving convergence in the presence of the stochastic gradient noise is non-trivial. Even with simple dynamics, significant physical intuition is often required to modify the dynamical system to account for the stochastic gradient noise. In this paper, we provide a general recipe for constructing MCMC samplers--including stochastic gradient versions--based on continuous Markov processes specified via two matrices. We constructively prove that the framework is complete. That is, any continuous Markov process that provides samples from the target distribution can be written in our framework. We show how previous continuous-dynamic samplers can be trivially "reinvented" in our framework, avoiding the complicated sampler-specific proofs. We likewise use our recipe to straightforwardly propose a new state-adaptive sampler: stochastic gradient Riemann Hamiltonian Monte Carlo (SGRHMC). Our experiments on simulated data and a streaming Wikipedia analysis demonstrate that the proposed SGRHMC sampler inherits the benefits of Riemann HMC, with the scalability of stochastic gradient methods.

Wednesday December 9, 2015 19:00 - 23:59

210 C #47

210 C #47

A Dual Augmented Block Minimization Framework for Learning with Limited Memory

In past few years, several techniques have been proposed for training of linear Support Vector Machine (SVM) in limited-memory setting, where a dual block-coordinate descent (dual-BCD) method was used to balance cost spent on I/O and computation. In this paper, we consider the more general setting of regularized \emph{Empirical Risk Minimization (ERM)} when data cannot fit into memory. In particular, we generalize the existing block minimization framework based on strong duality and \emph{Augmented Lagrangian} technique to achieve global convergence for ERM with arbitrary convex loss function and regularizer. The block minimization framework is flexible in the sense that, given a solver working under sufficient memory, one can integrate it with the framework to obtain a solver globally convergent under limited-memory condition. We conduct experiments on L1-regularized classification and regression problems to corroborate our convergence theory and compare the proposed framework to algorithms adopted from online and distributed settings, which shows superiority of the proposed approach on data of size ten times larger than the memory capacity.

Wednesday December 9, 2015 19:00 - 23:59

210 C #83

210 C #83

A Framework for Individualizing Predictions of Disease Trajectories by Exploiting Multi-Resolution Structure

For many complex diseases, there is a wide variety of ways in which an individual can manifest the disease. The challenge of personalized medicine is to develop tools that can accurately predict the trajectory of an individual's disease, which can in turn enable clinicians to optimize treatments. We represent an individual's disease trajectory as a continuous-valued continuous-time function describing the severity of the disease over time. We propose a hierarchical latent variable model that individualizes predictions of disease trajectories. This model shares statistical strength across observations at different resolutions--the population, subpopulation and the individual level. We describe an algorithm for learning population and subpopulation parameters offline, and an online procedure for dynamically learning individual-specific parameters. Finally, we validate our model on the task of predicting the course of interstitial lung disease, a leading cause of death among patients with the autoimmune disease scleroderma. We compare our approach against state-of-the-art and demonstrate significant improvements in predictive accuracy.

Wednesday December 9, 2015 19:00 - 23:59

210 C #21

210 C #21

A Generalization of Submodular Cover via the Diminishing Return Property on the Integer Lattice

We consider a generalization of the submodular cover problem based on the concept of diminishing return property on the integer lattice. We are motivated by real scenarios in machine learning that cannot be captured by (traditional) submodular set functions. We show that the generalized submodular cover problem can be applied to various problems and devise a bicriteria approximation algorithm. Our algorithm is guaranteed to output a log-factor approximate solution that satisfies the constraints with the desired accuracy. The running time of our algorithm is roughly $O(n\log (nr) \log{r})$, where $n$ is the size of the ground set and $r$ is the maximum value of a coordinate. The dependency on $r$ is exponentially better than the naive reduction algorithms. Several experiments on real and artificial datasets demonstrate that the solution quality of our algorithm is comparable to naive algorithms, while the running time is several orders of magnitude faster.

Wednesday December 9, 2015 19:00 - 23:59

210 C #86

210 C #86

A Normative Theory of Adaptive Dimensionality Reduction in Neural Networks

To make sense of the world our brains must analyze high-dimensional datasets streamed by our sensory organs. Because such analysis begins with dimensionality reduction, modelling early sensory processing requires biologically plausible online dimensionality reduction algorithms. Recently, we derived such an algorithm, termed similarity matching, from a Multidimensional Scaling (MDS) objective function. However, in the existing algorithm, the number of output dimensions is set a priori by the number of output neurons and cannot be changed. Because the number of informative dimensions in sensory inputs is variable there is a need for adaptive dimensionality reduction. Here, we derive biologically plausible dimensionality reduction algorithms which adapt the number of output dimensions to the eigenspectrum of the input covariance matrix. We formulate three objective functions which, in the offline setting, are optimized by the projections of the input dataset onto its principal subspace scaled by the eigenvalues of the output covariance matrix. In turn, the output eigenvalues are computed as i) soft-thresholded, ii) hard-thresholded, iii) equalized thresholded eigenvalues of the input covariance matrix. In the online setting, we derive the three corresponding adaptive algorithms and map them onto the dynamics of neuronal activity in networks with biologically plausible local learning rules. Remarkably, in the last two networks, neurons are divided into two classes which we identify with principal neurons and interneurons in biological circuits.

Wednesday December 9, 2015 19:00 - 23:59

210 C #41

210 C #41

A Reduced-Dimension fMRI Shared Response Model
Multi-subject fMRI data is critical for evaluating the generality and validity of findings across subjects, and its effective utilization helps improve analysis sensitivity. We develop a shared response model for aggregating multi-subject fMRI data that accounts for different functional topographies among anatomically aligned datasets. Our model demonstrates improved sensitivity in identifying a shared response for a variety of datasets and anatomical brain regions of interest. Furthermore, by removing the identified shared response, it allows improved detection of group differences. The ability to identify what is shared and what is not shared opens the model to a wide range of multi-subject fMRI studies.

Wednesday December 9, 2015 19:00 - 23:59

210 C #23

210 C #23

A Structural Smoothing Framework For Robust Graph Comparison

In this paper, we propose a general smoothing framework for graph kernels by taking \textit{structural similarity} into account, and apply it to derive smoothed variants of popular graph kernels. Our framework is inspired by state-of-the-art smoothing techniques used in natural language processing (NLP). However, unlike NLP applications which primarily deal with strings, we show how one can apply smoothing to a richer class of inter-dependent sub-structures that naturally arise in graphs. Moreover, we discuss extensions of the Pitman-Yor process that can be adapted to smooth structured objects thereby leading to novel graph kernels. Our kernels are able to tackle the diagonal dominance problem, while respecting the structural similarity between sub-structures, especially under the presence of edge or label noise. Experimental evaluation shows that not only our kernels outperform the unsmoothed variants, but also achieve statistically significant improvements in classification accuracy over several other graph kernels that have been recently proposed in literature. Our kernels are competitive in terms of runtime, and offer a viable option for practitioners.

Wednesday December 9, 2015 19:00 - 23:59

210 C #36

210 C #36

A Tractable Approximation to Optimal Point Process Filtering: Application to Neural Encoding
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal encoding/decoding strategies, which are of significant relevance to Computational Neuroscience. We develop an analytically tractable Bayesian approximation to optimal filtering based on point process observations, which allows us to introduce distributional assumptions about sensory cell properties, that greatly facilitates the analysis of optimal encoding in situations deviating from common assumptions of uniform coding. The analytic framework leads to insights which are difficult to obtain from numerical algorithms, and is consistent with experiments about the distribution of tuning curve centers. Interestingly, we find that the information gained from the absence of spikes may be crucial to performance.

Wednesday December 9, 2015 19:00 - 23:59

210 C #26

210 C #26

A Universal Catalyst for First-Order Optimization

We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective by approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. This strategy applies to a large class of algorithms, including gradient descent, block coordinate descent, SAG, SAGA, SDCA, SVRG, Finito/MISO, and their proximal variants. For all of these methods, we provide acceleration and explicit support for non-strongly convex objectives. In addition to theoretical speed-up, we also show that acceleration is useful in practice, especially for ill-conditioned problems where we measure significant improvements.

Wednesday December 9, 2015 19:00 - 23:59

210 C #87

210 C #87

Accelerated Mirror Descent in Continuous and Discrete Time
We study accelerated mirror descent dynamics in continuous and discrete time. Combining the original continuous-time motivation of mirror descent with a recent ODE interpretation of Nesterov's accelerated method, we propose a family of continuous-time descent dynamics for convex functions with Lipschitz gradients, such that the solution trajectories are guaranteed to converge to the optimum at a $O(1/t^2)$ rate. We then show that a large family of first-order accelerated methods can be obtained as a discretization of the ODE, and these methods converge at a $O(1/k^2)$ rate. This connection between accelerated mirror descent and the ODE provides an intuitive approach to the design and analysis of accelerated first-order algorithms.

Wednesday December 9, 2015 19:00 - 23:59

210 C #96

210 C #96

Action-Conditional Video Prediction using Deep Networks in Atari Games
Motivated by vision-based reinforcement learning (RL) problems, in particular Atari games from the recent benchmark Aracade Learning Environment (ALE), we consider spatio-temporal prediction problems where future (image-)frames are dependent on control variables or actions as well as previous frames. While not composed of natural scenes, frames in Atari games are high-dimensional in size, can involve tens of objects with one or more objects being controlled by the actions directly and many other objects being influenced indirectly, can involve entry and departure of objects, and can involve deep partial observability. We propose and evaluate two deep neural network architectures that consist of encoding, action-conditional transformation, and decoding layers based on convolutional neural networks and recurrent neural networks. Experimental results show that the proposed architectures are able to generate visually-realistic frames that are also useful for control over approximately 100-step action-conditional futures in some games. To the best of our knowledge, this paper is the first to make and evaluate long-term predictions on high-dimensional video conditioned by control inputs.

Wednesday December 9, 2015 19:00 - 23:59

210 C #18

210 C #18

Adaptive Online Learning
We propose a general framework for studying adaptive regret bounds in the online learning setting, subsuming model selection and data-dependent bounds. Given a data- or model-dependent bound we ask, “Does there exist some algorithm achieving this bound?” We show that modifications to recently introduced sequential complexity measures can be used to answer this question by providing sufficient conditions under which adaptive rates can be achieved. In particular each adaptive rate induces a set of so-called offset complexity measures, and obtaining small upper bounds on these quantities is sufficient to demonstrate achievability. A cornerstone of our analysis technique is the use of one-sided tail inequalities to bound suprema of offset random processes.Our framework recovers and improves a wide variety of adaptive bounds including quantile bounds, second order data-dependent bounds, and small loss bounds. In addition we derive a new type of adaptive bound for online linear optimization based on the spectral norm, as well as a new online PAC-Bayes theorem.

Wednesday December 9, 2015 19:00 - 23:59

210 C #100

210 C #100

Approximating Sparse PCA from Incomplete Data

We study how well one can recover sparse principal componentsof a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems,if the sketch is close (in the spectral norm) to the original datamatrix, then one can recover a near optimal solution to the optimizationproblem by using the sketch. In particular, we use this approach toobtain sparse principal components and show that for \math{m} data pointsin \math{n} dimensions,\math{O(\epsilon^{-2}\tilde k\max\{m,n\})} elements gives an\math{\epsilon}-additive approximation to the sparse PCA problem(\math{\tilde k} is the stable rank of the data matrix).We demonstrate our algorithms extensivelyon image, text, biological and financial data.The results show that not only are we able to recover the sparse PCAs from the incomplete data, but by using our sparse sketch, the running timedrops by a factor of five or more.

Wednesday December 9, 2015 19:00 - 23:59

210 C #62

210 C #62

Associative Memory via a Sparse Recovery Model

An associative memory is a structure learned from a dataset $\mathcal{M}$ of vectors (signals) in a way such that, given a noisy version of one of the vectors as input, the nearest valid vector from $\mathcal{M}$ (nearest neighbor) is provided as output, preferably via a fast iterative algorithm. Traditionally, binary (or $q$-ary) Hopfield neural networks are used to model the above structure. In this paper, for the first time, we propose a model of associative memory based on sparse recovery of signals. Our basic premise is simple. For a dataset, we learn a set of linear constraints that every vector in the dataset must satisfy. Provided these linear constraints possess some special properties, it is possible to cast the task of finding nearest neighbor as a sparse recovery problem. Assuming generic random models for the dataset, we show that it is possible to store super-polynomial or exponential number of $n$-length vectors in a neural network of size $O(n)$. Furthermore, given a noisy version of one of the stored vectors corrupted in near-linear number of coordinates, the vector can be correctly recalled using a neurally feasible algorithm.

Wednesday December 9, 2015 19:00 - 23:59

210 C #74

210 C #74

Attention-Based Models for Speech Recognition
Recurrent sequence generators conditioned on input data through an attention mechanism have recently shown very good performance on a range of tasks including machine translation, handwriting synthesis and image caption generation. We extend the attention-mechanism with features needed for speech recognition. We show that while an adaptation of the model used for machine translation reaches a competitive 18.6\% phoneme error rate (PER) on the TIMIT phoneme recognition task, it can only be applied to utterances which are roughly as long as the ones it was trained on. We offer a qualitative explanation of this failure and propose a novel and generic method of adding location-awareness to the attention mechanism to alleviate this issue. The new method yields a model that is robust to long inputs and achieves 18\% PER in single utterances and 20\% in 10-times longer (repeated) utterances. Finally, we propose a change to the attention mechanism that prevents it from concentrating too much on single frames, which further reduces PER to 17.6\% level.

Wednesday December 9, 2015 19:00 - 23:59

210 C #5

210 C #5

Attractor Network Dynamics Enable Preplay and Rapid Path Planning in Maze–like Environments
Rodents navigating in a well-known environment can rapidly learn and revisit observed reward locations, often after a single trial. While the mechanism for rapid path planning is unknown, the CA3 region in the hippocampus plays an important role, and emerging evidence suggests that place cell activity during hippocampal "preplay" periods may trace out future goal-directed trajectories. Here, we show how a particular mapping of space allows for the immediate generation of trajectories between arbitrary start and goal locations in an environment, based only on the mapped representation of the goal. We show that this representation can be implemented in a neural attractor network model, resulting in bump--like activity profiles resembling those of the CA3 region of hippocampus. Neurons tend to locally excite neurons with similar place field centers, while inhibiting other neurons with distant place field centers, such that stable bumps of activity can form at arbitrary locations in the environment. The network is initialized to represent a point in the environment, then weakly stimulated with an input corresponding to an arbitrary goal location. We show that the resulting activity can be interpreted as a gradient ascent on the value function induced by a reward at the goal location. Indeed, in networks with large place fields, we show that the network properties cause the bump to move smoothly from its initial location to the goal, around obstacles or walls. Our results illustrate that an attractor network with hippocampal-like attributes may be important for rapid path planning.

Wednesday December 9, 2015 19:00 - 23:59

210 C #10

210 C #10

Backpropagation for Energy-Efficient Neuromorphic Computing
Solving real world problems with embedded neural networks requires both training algorithms that achieve high performance and compatible hardware that runs in real time while remaining energy efficient. For the former, deep learning using backpropagation has recently achieved a string of successes across many domains and datasets. For the latter, neuromorphic chips that run spiking neural networks have recently achieved unprecedented energy efficiency. To bring these two advances together, we must first resolve the incompatibility between backpropagation, which uses continuous-output neurons and synaptic weights, and neuromorphic designs, which employ spiking neurons and discrete synapses. Our approach is to treat spikes and discrete synapses as continuous probabilities, which allows training the network using standard backpropagation. The trained network naturally maps to neuromorphic hardware by sampling the probabilities to create one or more networks, which are merged using ensemble averaging. To demonstrate, we trained a sparsely connected network that runs on the TrueNorth chip using the MNIST dataset. With a high performance network (ensemble of $64$), we achieve $99.42\%$ accuracy at $121 \mu$J per image, and with a high efficiency network (ensemble of $1$) we achieve $92.7\%$ accuracy at $0.408 \mu$J per image.

Wednesday December 9, 2015 19:00 - 23:59

210 C #13

210 C #13

Bandit Smooth Convex Optimization: Improving the Bias-Variance Tradeoff
Bandit convex optimization is one of the fundamental problems in the field of online learning. The best algorithm for the general bandit convex optimization problem guarantees a regret of $\widetilde{O}(T^{5/6})$, while the best known lower bound is $\Omega(T^{1/2})$. Many attemptshave been made to bridge the huge gap between these bounds. A particularly interesting special case of this problem assumes that the loss functions are smooth. In this case, the best known algorithm guarantees a regret of $\widetilde{O}(T^{2/3})$. We present an efficient algorithm for the banditsmooth convex optimization problem that guarantees a regret of $\widetilde{O}(T^{5/8})$. Our result rules out an $\Omega(T^{2/3})$ lower bound and takes a significant step towards the resolution of this open problem.

Wednesday December 9, 2015 19:00 - 23:59

210 C #98

210 C #98

Barrier Frank-Wolfe for Marginal Inference

We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the marginal polytope through repeated maximum a posteriori (MAP) calls. This modular structure enables us to leverage black-box MAP solvers (both exact and approximate) for variational inference, and obtains more accurate results than tree-reweighted algorithms that optimize over the local consistency relaxation. Theoretically, we bound the sub-optimality for the proposed algorithm despite the TRW objective having unbounded gradients at the boundary of the marginal polytope. Empirically, we demonstrate the increased quality of results found by tightening the relaxation over the marginal polytope as well as the spanning tree polytope on synthetic and real-world instances.

Wednesday December 9, 2015 19:00 - 23:59

210 C #48

210 C #48

Bayesian Active Model Selection with an Application to Automated Audiometry

We introduce a novel information-theoretic approach for active model selection and demonstrate its effectiveness in a real-world application. Although our method can work with arbitrary models, we focus on actively learning the appropriate structure for Gaussian process (GP) models with arbitrary observation likelihoods. We then apply this framework to rapid screening for noise-induced hearing loss (NIHL), a widespread and preventible disability, if diagnosed early. We construct a GP model for pure-tone audiometric responses of patients with NIHL. Using this and a previously published model for healthy responses, the proposed method is shown to be capable of diagnosing the presence or absence of NIHL with drastically fewer samples than existing approaches. Further, the method is extremely fast and enables the diagnosis to be performed in real time.

Wednesday December 9, 2015 19:00 - 23:59

210 C #19

210 C #19

Beyond Sub-Gaussian Measurements: High-Dimensional Structured Estimation with Sub-Exponential Designs

We consider the problem of high-dimensional structured estimation with norm-regularized estimators, such as Lasso, when the design matrix and noise are drawn from sub-exponential distributions.Existing results only consider sub-Gaussian designs and noise, and both the sample complexity and non-asymptotic estimation error have been shown to depend on the Gaussian width of suitable sets. In contrast, for the sub-exponential setting, we show that the sample complexity and the estimation error will depend on the exponential width of the corresponding sets, and the analysis holds for any norm. Further, using generic chaining, we show that the exponential width for any set will be at most $\sqrt{\log p}$ times the Gaussian width of the set, yielding Gaussian width based results even for the sub-exponential case. Further, for certain popular estimators, viz Lasso and Group Lasso, using a VC-dimension based analysis, we show that the sample complexity will in fact be the same order as Gaussian designs. Our general analysis and results are the first in the sub-exponential setting, and are readily applicable to special sub-exponential families such as log-concave and extreme-value distributions.

Wednesday December 9, 2015 19:00 - 23:59

210 C #99

210 C #99

Bounding errors of Expectation-Propagation

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic interpretation in the number n of datapoints, which allows us to study EP's convergence with respect to the true posterior. In particular, we show that EP converges at a rate of $O(n^{-2})$ for the mean, up to an order of magnitude faster than the traditional Gaussian approximation at the mode. We also give similar asymptotic expansions for moments of order 2 to 4, as well as excess Kullback-Leibler cost (defined as the additional KL cost incurred by using EP rather than the ideal Gaussian approximation). All these expansions highlight the superior convergence properties of EP. Our approach for deriving those results is likely applicable to many similar approximate inference methods. In addition, we introduce bounds on the moments of log-concave distributions that may be of independent interest.

Wednesday December 9, 2015 19:00 - 23:59

210 C #70

210 C #70

Color Constancy by Learning to Predict Chromaticity from Luminance
Color constancy is the recovery of true surface color from observed color, and requires estimating the chromaticity of scene illumination to correct for the bias it induces. In this paper, we show that the per-pixel color statistics of natural scenes---without any spatial or semantic context---can by themselves be a powerful cue for color constancy. Specifically, we describe an illuminant estimation method that is built around a "classifier" for identifying the true chromaticity of a pixel given its luminance (absolute brightness across color channels). During inference, each pixel's observed color restricts its true chromaticity to those values that can be explained by one of a candidate set of illuminants, and applying the classifier over these values yields a distribution over the corresponding illuminants. A global estimate for the scene illuminant is computed through a simple aggregation of these distributions across all pixels. We begin by simply defining the luminance-to-chromaticity classifier by computing empirical histograms over discretized chromaticity and luminance values from a training set of natural images. These histograms reflect a preference for hues corresponding to smooth reflectance functions, and for achromatic colors in brighter pixels. Despite its simplicity, the resulting estimation algorithm outperforms current state-of-the-art color constancy methods. Next, we propose a method to learn the luminance-to-chromaticity classifier "end-to-end". Using stochastic gradient descent, we set chromaticity-luminance likelihoods to minimize errors in the final scene illuminant estimates on a training set. This leads to further improvements in accuracy, most significantly in the tail of the error distribution.

Wednesday December 9, 2015 19:00 - 23:59

210 C #16

210 C #16

Consistent Multilabel Classification

Multilabel classification is rapidly developing as an important aspect of modern predictive modeling, motivating study of its theoretical aspects. To this end, we propose a framework for constructing and analyzing multilabel classification metrics which reveals novel results on a parametric form for population optimal classifiers, and additional insight into the role of label correlations. In particular, we show that for multilabel metrics constructed as instance-, micro- and macro-averages, the population optimal classifier can be decomposed into binary classifiers based on the marginal instance-conditional distribution of each label, with a weak association between labels via the threshold. Thus, our analysis extends the state of the art from a few known multilabel classification metrics such as Hamming loss, to a general framework applicable to many of the classification metrics in common use. Based on the population-optimal classifier, we propose a computationally efficient and general-purpose plug-in classification algorithm, and prove its consistency with respect to the metric of interest. Empirical results on synthetic and benchmark datasets are supportive of our theoretical findings.

Wednesday December 9, 2015 19:00 - 23:59

210 C #39

210 C #39

Convergence Rates of Active Learning for Maximum Likelihood Estimation

An active learner is given a class of models, a large set of unlabeled examples, and the ability to interactively query labels of a subset of these examples; the goal of the learner is to learn a model in the class that fits the data well. Previous theoretical work has rigorously characterized label complexity of active learning, but most of this work has focused on the PAC or the agnostic PAC model. In this paper, we shift our attention to a more general setting -- maximum likelihood estimation. Provided certain conditions hold on the model class, we provide a two-stage active learning algorithm for this problem. The conditions we require are fairly general, and cover the widely popular class of Generalized Linear Models, which in turn, include models for binary and multi-class classification, regression, and conditional random fields. We provide an upper bound on the label requirement of our algorithm, and a lower bound that matches it up to lower order terms. Our analysis shows that unlike binary classification in the realizable case, just a single extraround of interaction is sufficient to achieve near-optimal performance in maximum likelihood estimation. On the empirical side, the recent work in (Gu et al. 2012) and (Gu et al. 2014) (on active linear and logistic regression) shows the promise of this approach.

Wednesday December 9, 2015 19:00 - 23:59

210 C #80

210 C #80

Convergence rates of sub-sampled Newton methods

We consider the problem of minimizing a sum of $n$ functions via projected iterations onto a convex parameter set $\C \subset \reals^p$, where $n\gg p\gg 1$. In this regime, algorithms which utilize sub-sampling techniques are known to be effective.In this paper, we use sub-sampling techniques together with low-rank approximation to design a new randomized batch algorithm which possesses comparable convergence rate to Newton's method, yet has much smaller per-iteration cost. The proposed algorithm is robust in terms of starting point and step size, and enjoys a composite convergence rate, namely, quadratic convergence at start and linear convergence when the iterate is close to the minimizer. We develop its theoretical analysis which also allows us to select near-optimal algorithm parameters. Our theoretical results can be used to obtain convergence rates of previously proposed sub-sampling based algorithms as well. We demonstrate how our results apply to well-known machine learning problems.Lastly, we evaluate the performance of our algorithm on several datasets under various scenarios.

Wednesday December 9, 2015 19:00 - 23:59

210 C #77

210 C #77

Decoupled Deep Neural Network for Semi-supervised Semantic Segmentation
We propose a novel deep neural network architecture for semi-supervised semantic segmentation using heterogeneous annotations. Contrary to existing approaches posing semantic segmentation as region-based classification, our algorithm decouples classification and segmentation, and learns a separate network for each task. In this architecture, labels associated with an image are identified by classification network, and binary segmentation is subsequently performed for each identified label by segmentation network. The decoupled architecture enables us to learn classification and segmentation networks separately based on the training data with image-level and pixel-wise class labels, respectively. It facilitates to reduce search space for segmentation effectively by exploiting class-specific activation maps obtained from bridging layers. Our algorithm shows outstanding performance compared to other semi-supervised approaches even with much less training images with strong annotations in PASCAL VOC dataset.

Wednesday December 9, 2015 19:00 - 23:59

210 C #17

210 C #17

Deep Convolutional Inverse Graphics Network
This paper presents the Deep Convolution Inverse Graphics Network (DC-IGN), a model that aims to learn an interpretable representation of images, disentangled with respect to three-dimensional scene structure and viewing transformations such as depth rotations and lighting variations. The DC-IGN model is composed of multiple layers of convolution and de-convolution operators and is trained using the Stochastic Gradient Variational Bayes (SGVB) algorithm. We propose a training procedure to encourage neurons in the graphics code layer to represent a specific transformation (e.g. pose or light). Given a single input image, our model can generate new images of the same object with variations in pose and lighting. We present qualitative and quantitative tests of the model's efficacy at learning a 3D rendering engine for varied object classes including faces and chairs.

Wednesday December 9, 2015 19:00 - 23:59

210 C #6

210 C #6

Deep Visual Analogy-Making
In addition to identifying the content within a single image, relating images and generating related images are critical tasks for image understanding. Recently, deep convolutional networks have yielded breakthroughs in producing image labels, annotations and captions, but have only just begun to be used for producing high-quality image outputs. In this paper we develop a novel deep network trained end-to-end to perform visual analogy making, which is the task of transforming a query image according to an example pair of related images. Solving this problem requires both accurately recognizing a visual relationship and generating a transformed query image accordingly. Inspired by recent advances in language modeling, we propose to solve visual analogies by learning to map images to a neural embedding in which analogical reasoning is simple, such as by vector subtraction and addition. In experiments, our model effectively models visual analogies on several datasets: 2D shapes, animated video game sprites, and 3D car models.

Wednesday December 9, 2015 19:00 - 23:59

210 C #1

210 C #1

Efficient and Robust Automated Machine Learning

The success of machine learning in a broad range of applications has led to an ever-growing demand for machine learning systems that can be used off the shelf by non-experts. To be effective in practice, such systems need to automatically choose a good algorithm and feature preprocessing steps for a new dataset at hand, and also set their respective hyperparameters. Recent work has started to tackle this automated machine learning (AutoML) problem with the help of efficient Bayesian optimization methods. In this work we introduce a robust new AutoML system based on scikit-learn (using 15 classifiers, 14 feature preprocessing methods, and 4 data preprocessing methods, giving rise to a structured hypothesis space with 110 hyperparameters). This system, which we dub auto-sklearn, improves on existing AutoML methods by automatically taking into account past performance on similar datasets, and by constructing ensembles from the models evaluated during the optimization. Our system won the first phase of the ongoing ChaLearn AutoML challenge, and our comprehensive analysis on over 100 diverse datasets shows that it substantially outperforms the previous state of the art in AutoML. We also demonstrate the performance gains due to each of our contributions and derive insights into the effectiveness of the individual components of auto-sklearn.

Wednesday December 9, 2015 19:00 - 23:59

210 C #20

210 C #20

Efficient Exact Gradient Update for training Deep Networks with Very Large Sparse Targets
An important class of problems involves training deep neural networks with sparse prediction targets of very high dimension D. These occur naturally in e.g. neural language models or the learning of word-embeddings, often posed as predicting the probability of next words among a vocabulary of size D (e.g. 200,000). Computing the equally large, but typically non-sparse D-dimensional output vector from a last hidden layer of reasonable dimension d (e.g. 500) incurs a prohibitive $O(Dd)$ computational cost for each example, as does updating the $D \times d$ output weight matrix and computing the gradient needed for backpropagation to previous layers. While efficient handling of large sparse network inputs is trivial, this case of large sparse targets is not, and has thus so far been sidestepped with approximate alternatives such as hierarchical softmax or sampling-based approximations during training. In this work we develop an original algorithmic approach that, for a family of loss functions that includes squared error and spherical softmax, can compute the exact loss, gradient update for the output weights, and gradient for backpropagation, all in $O(d^2)$ per example instead of $O(Dd)$, remarkably without ever computing the D-dimensional output. The proposed algorithm yields a speedup of $\frac{D}{4d}$, i.e. two orders of magnitude for typical sizes, for that critical part of the computations that often dominates the training time in this kind of network architecture.

Wednesday December 9, 2015 19:00 - 23:59

210 C #24

210 C #24

Efficient Non-greedy Optimization of Decision Trees

Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy procedure often leads to suboptimal trees. In this paper, we present an algorithm for optimizing the split functions at all levels of the tree jointly with the leaf parameters, based on a global objective. We show that the problem of finding optimal linear-combination (oblique) splits for decision trees is related to structured prediction with latent variables, and we formulate a convex-concave upper bound on the tree's empirical loss. Computing the gradient of the proposed surrogate objective with respect to each training exemplar is O(d^2), where d is the tree depth, and thus training deep trees is feasible. The use of stochastic gradient descent for optimization enables effective training with large datasets. Experiments on several classification benchmarks demonstrate that the resulting non-greedy decision trees outperform greedy decision tree baselines.

Wednesday December 9, 2015 19:00 - 23:59

210 C #42

210 C #42

Efficient Output Kernel Learning for Multiple Tasks

The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other. While previously the relationship between tasks had to be user-defined in the form of an output kernel, recent approaches jointly learn the tasks and the output kernel. As the output kernel is a positive semidefinite matrix, the resulting optimization problems are not scalable in the number of tasks as an eigendecomposition is required in each step. Using the theory of positive semidefinite kernels we show in this paper that for a certain class of regularizers on the output kernel, the constraint of being positive semidefinite can be dropped as it is automatically satisfied for the relaxed problem. This leads to an unconstrained dual problem which can be solved efficiently. Experiments on several multi-task and multi-class data sets illustrate the efficacy of our approach in terms of computational efficiency as well as generalization performance.

Wednesday December 9, 2015 19:00 - 23:59

210 C #54

210 C #54

Empirical Localization of Homogeneous Divergences on Discrete Sample Spaces
In this paper, we propose a novel parameter estimator for probabilistic models on discrete space. The proposed estimator is derived from minimization of homogeneous divergence and can be constructed without calculation of the normalization constant, which is frequently infeasible for models in the discrete space. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality, and reveal a relationship with the alpha-divergence. Small experiments show that the proposed estimator attains comparable performance to the MLE with drastically lower computational cost.

Wednesday December 9, 2015 19:00 - 23:59

210 C #58

210 C #58

End-To-End Memory Networks
We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

Wednesday December 9, 2015 19:00 - 23:59

210 C #7

210 C #7

Equilibrated adaptive learning rates for non-convex optimization
Parameter-specific adaptive learning rate methods are computationally efficient ways to reduce the ill-conditioning problems encountered when training large deep networks. Following recent work that strongly suggests that most of thecritical points encountered when training such networks are saddle points, we find how considering the presence of negative eigenvalues of the Hessian could help us design better suited adaptive learning rate schemes. We show that the popular Jacobi preconditioner has undesirable behavior in the presence of both positive and negative curvature, and present theoretical and empirical evidence that the so-called equilibration preconditioner is comparatively better suited to non-convex problems. We introduce a novel adaptive learning rate scheme, called ESGD, based on the equilibration preconditioner. Our experiments demonstrate that both schemes yield very similar step directions but that ESGD sometimes surpasses RMSProp in terms of convergence speed, always clearly improving over plain stochastic gradient descent.

Wednesday December 9, 2015 19:00 - 23:59

210 C #27

210 C #27

Exactness of Approximate MAP Inference in Continuous MRFs

Computing the MAP assignment in graphical models is generally intractable. As a result, for discrete graphical models, the MAP problem is often approximated using linear programming relaxations. Much research has focused on characterizing when these LP relaxations are tight, and while they are relatively well-understood in the discrete case, only a few results are known for their continuous analog. In this work, we use graph covers to provide necessary and sufficient conditions for continuous MAP relaxations to be tight. We use this characterization to give simple proofs that the relaxation is tight for log-concave decomposable and log-supermodular decomposable models. We conclude by exploring the relationship between these two seemingly distinct classes of functions and providing specific conditions under which the MAP relaxation can and cannot be tight.

Wednesday December 9, 2015 19:00 - 23:59

210 C #91

210 C #91

Fast and Memory Optimal Low-Rank Matrix Approximation

In this paper, we revisit the problem of constructing a near-optimal rank $k$ approximation of a matrix $M\in [0,1]^{m\times n}$ under the streaming data model where the columns of $M$ are revealed sequentially. We present SLA (Streaming Low-rank Approximation), an algorithm that is asymptotically accurate, when $k s_{k+1} (M) = o(\sqrt{mn})$ where $s_{k+1}(M)$ is the $(k+1)$-th largest singular value of $M$. This means that its average mean-square error converges to 0 as $m$ and $n$ grow large (i.e., $\|\hat{M}^{(k)}-M^{(k)} \|_F^2 = o(mn)$ with high probability, where $\hat{M}^{(k)}$ and $M^{(k)}$ denote the output of SLA and the optimal rank $k$ approximation of $M$, respectively). Our algorithm makes one pass on the data if the columns of $M$ are revealed in a random order, and two passes if the columns of $M$ arrive in an arbitrary order. To reduce its memory footprint and complexity, SLA uses random sparsification, and samples each entry of $M$ with a small probability $\delta$. In turn, SLA is memory optimal as its required memory space scales as $k(m+n)$, the dimension of its output. Furthermore, SLA is computationally efficient as it runs in $O(\delta kmn)$ time (a constant number of operations is made for each observed entry of $M$), which can be as small as $O(k\log(m)^4 n)$ for an appropriate choice of $\delta$ and if $n\ge m$.

Wednesday December 9, 2015 19:00 - 23:59

210 C #88

210 C #88

Finite-Time Analysis of Projected Langevin Monte Carlo

We analyze the projected Langevin Monte Carlo (LMC) algorithm, a close cousin of projected Stochastic Gradient Descent (SGD). We show that LMC allows to sample in polynomial time from a posterior distribution restricted to a convex body and with concave log-likelihood. This gives the first Markov chain to sample from a log-concave distribution with a first-order oracle, as the existing chains with provable guarantees (lattice walk, ball walk and hit-and-run) require a zeroth-order oracle. Our proof uses elementary concepts from stochastic calculus which could be useful more generally to understand SGD and its variants.

Wednesday December 9, 2015 19:00 - 23:59

210 C #93

210 C #93

Fixed-Length Poisson MRF: Adding Dependencies to the Multinomial

We propose a novel distribution that generalizes the Multinomial distribution to enable dependencies between dimensions. Our novel distribution is based on the parametric form of the Poisson MRF model [Yang et al., 2012] but is fundamentally different because of the domain restriction to a fixed-length vector like in a Multinomial where the number of trials is fixed or known. Thus, we propose the Fixed-Length Poisson MRF (LPMRF) distribution. We develop methods to estimate the likelihood and log partition function (i.e. the log normalizing constant), which was not possible with the Poisson MRF model. In addition, we propose novel mixture and topic models that use LPMRF as a base distribution and discuss the similarities and differences with previous topic models such as the recently proposed Admixture of Poisson MRFs [Inouye et al., 2014]. We show the effectiveness of our LPMRF distribution over Multinomial models by evaluating the test set perplexity on a dataset of abstracts and Wikipedia. Qualitatively, we show that the positive dependencies discovered by LPMRF are interesting and intuitive. Finally, we show that our algorithms are fast and have good scaling.

Wednesday December 9, 2015 19:00 - 23:59

210 C #32

210 C #32

Gaussian Process Random Fields

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via pairwise potentials. The GPRF likelihood is a simple, tractable, and parallelizeable approximation to the full GP marginal likelihood, enabling latent variable modeling and hyperparameter selection on large datasets. We demonstrate its effectiveness on synthetic spatial data as well as a real-world application to seismic event location.

Wednesday December 9, 2015 19:00 - 23:59

210 C #29

210 C #29

Gradient Estimation Using Stochastic Computation Graphs

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external world. Estimating the gradient of this loss function, using samples, lies at the core of gradient-based learning algorithms for these problems. We introduce the formalism of stochastic computation graphs--directed acyclic graphs that include both deterministic functions and conditional probability distributions and describe how to easily and automatically derive an unbiased estimator of the loss function's gradient. The resulting algorithm for computing the gradient estimator is a simple modification of the standard backpropagation algorithm. The generic scheme we propose unifies estimators derived in variety of prior work, along with variance-reduction techniques therein. It could assist researchers in developing intricate models involving a combination of stochastic and deterministic operations, enabling, for example, attention, memory, and control actions.

Wednesday December 9, 2015 19:00 - 23:59

210 C #55

210 C #55

Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families

We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns the target's gradient structure by fitting an exponential family model in a Reproducing Kernel Hilbert Space. Computational costs are reduced by two novel efficient approximations to this gradient. While being asymptotically exact, KMC mimics HMC in terms of sampling efficiency, and offers substantial mixing improvements over state-of-the-art gradient free samplers. We support our claims with experimental studies on both toy and real-world applications, including Approximate Bayesian Computation and exact-approximate MCMC.

Wednesday December 9, 2015 19:00 - 23:59

210 C #46

210 C #46

High Dimensional EM Algorithm: Statistical Optimization and Asymptotic Normality

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geometric rate and attains an estimator with the (near-)optimal statistical rate of convergence. (ii) Based on the obtained estimator, we propose a new inferential procedure for testing hypotheses for low dimensional components of high dimensional parameters. For a broad family of statistical models, our framework establishes the first computationally feasible approach for optimal estimation and asymptotic inference in high dimensions.

Wednesday December 9, 2015 19:00 - 23:59

210 C #73

210 C #73

Human Memory Search as Initial-Visit Emitting Random Walk

Imagine a random walk that outputs a state only when visiting it for the first time. The observed output is therefore a repeat-censored version of the underlying walk, and consists of a permutation of the states or a prefix of it. We call this model initial-visit emitting random walk (INVITE). Prior work has shown that the random walks with such a repeat-censoring mechanism explain well human behavior in memory search tasks, which is of great interest in both the study of human cognition and various clinical applications. However, parameter estimation in INVITE is challenging, because naive likelihood computation by marginalizing over infinitely many hidden random walk trajectories is intractable. In this paper, we propose the first efficient maximum likelihood estimate (MLE) for INVITE by decomposing the censored output into a series of absorbing random walks. We also prove theoretical properties of the MLE including identifiability and consistency. We show that INVITE outperforms several existing methods on real-world human response data from memory search tasks.

Wednesday December 9, 2015 19:00 - 23:59

210 C #33

210 C #33

Inferring Algorithmic Patterns with Stack-Augmented Recurrent Nets
Despite the recent achievements in machine learning, we are still very far from achieving real artificial intelligence. In this paper, we discuss the limitations of standard deep learning approaches and show that some of these limitations can be overcome by learning how to grow the complexity of a model in a structured way. Specifically, we study the simplest sequence prediction problems that are beyond the scope of what is learnable with standard recurrent networks, algorithmically generated sequences which can only be learned by models which have the capacity to count and to memorize sequences. We show that some basic algorithms can be learned from sequential data using a recurrent network associated with a trainable memory.

Wednesday December 9, 2015 19:00 - 23:59

210 C #9

210 C #9

Information-theoretic lower bounds for convex optimization with erroneous oracles
We consider the problem of optimizing convex and concave functions with access to an erroneous zeroth-order oracle. In particular, for a given function $x \to f(x)$ we consider optimization when one is given access to absolute error oracles that return values in [f(x) - \epsilon,f(x)+\epsilon] or relative error oracles that return value in [(1+\epsilon)f(x), (1 +\epsilon)f (x)], for some \epsilon larger than 0. We show stark information theoretic impossibility results for minimizing convex functions and maximizing concave functions over polytopes in this model.

Wednesday December 9, 2015 19:00 - 23:59

210 C #97

210 C #97

Inverse Reinforcement Learning with Locally Consistent Reward Functions

Existing inverse reinforcement learning (IRL) algorithms have assumed each expert’s demonstrated trajectory to be produced by only a single reward function. This paper presents a novel generalization of the IRL problem that allows each trajectory to be generated by multiple locally consistent reward functions, hence catering to more realistic and complex experts’ behaviors. Solving our generalized IRL problem thus involves not only learning these reward functions but also the stochastic transitions between them at any state (including unvisited states). By representing our IRL problem with a probabilistic graphical model, an expectation-maximization (EM) algorithm can be devised to iteratively learn the different reward functions and the stochastic transitions between them in order to jointly improve the likelihood of the expert’s demonstrated trajectories. As a result, the most likely partition of a trajectory into segments that are generated from different locally consistent reward functions selected by EM can be derived. Empirical evaluation on synthetic and real-world datasets shows that our IRL algorithm outperforms the state-of-the-art EM clustering with maximum likelihood IRL, which is, interestingly, a reduced variant of our approach.

Wednesday December 9, 2015 19:00 - 23:59

210 C #38

210 C #38

Is Approval Voting Optimal Given Approval Votes?

Some crowdsourcing platforms ask workers to express their opinions by approving a set of k good alternatives. It seems that the only reasonable way to aggregate these k-approval votes is the approval voting rule, which simply counts the number of times each alternative was approved. We challenge this assertion by proposing a probabilistic framework of noisy voting, and asking whether approval voting yields an alternative that is most likely to be the best alternative, given k-approval votes. While the answer is generally positive, our theoretical and empirical results call attention to situations where approval voting is suboptimal.

Wednesday December 9, 2015 19:00 - 23:59

210 C #40

210 C #40

Kullback-Leibler Proximal Variational Inference

We propose a new variational inference method based on the Kullback-Leibler (KL) proximal term. We make two contributions towards improving efficiency of variational inference. Firstly, we derive a KL proximal-point algorithm and show its equivalence to gradient descent with natural gradient in stochastic variational inference. Secondly, we use the proximal framework to derive efficient variational algorithms for non-conjugate models. We propose a splitting procedure to separate non-conjugate terms from conjugate ones. We then linearize the non-conjugate terms and show that the resulting subproblem admits a closed-form solution. Overall, our approach converts a non-conjugate model to subproblems that involve inference in well-known conjugate models. We apply our method to many models and derive generalizations for non-conjugate exponential family. Applications to real-world datasets show that our proposed algorithms are easy to implement, fast to converge, perform well, and reduce computations.

Wednesday December 9, 2015 19:00 - 23:59

210 C #51

210 C #51

Learning Causal Graphs with Small Interventions

We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previous work has focused on the use of separating systems for complete graphs for this task. We prove that any deterministic adaptive algorithm needs to be a separating system in order to learn complete graphs in the worst case. In addition, we present a novel separating system construction, whose size is close to optimal and is arguably simpler than previous work in combinatorics. We also develop a novel information theoretic lower bound on the number of interventions that applies in full generality, including for randomized adaptive learning algorithms. For general chordal graphs, we derive worst case lower bounds on the number of interventions. Building on observations about induced trees, we give a new deterministic adaptive algorithm to learn directions on any chordal skeleton completely. In the worst case, our achievable scheme is an $\alpha$-approximation algorithm where $\alpha$ is the independence number of the graph. We also show that there exist graph classes for which the sufficient number of experiments is close to the lower bound. In the other extreme, there are graph classes for which the required number of experiments is multiplicatively $\alpha$ away from our lower bound. In simulations, our algorithm almost always performs very close to the lower bound, while the approach based on separating systems for complete graphs is significantly worse for random chordal graphs.

Wednesday December 9, 2015 19:00 - 23:59

210 C #67

210 C #67

Learning Large-Scale Poisson DAG Models based on OverDispersion Scoring

In this paper, we address the question of identifiability and learning algorithms for large-scale Poisson Directed Acyclic Graphical (DAG) models. We define general Poisson DAG models as models where each node is a Poisson random variable with rate parameter depending on the values of the parents in the underlying DAG. First, we prove that Poisson DAG models are identifiable from observational data, and present a polynomial-time algorithm that learns the Poisson DAG model under suitable regularity conditions. The main idea behind our algorithm is based on overdispersion, in that variables that are conditionally Poisson are overdispersed relative to variables that are marginally Poisson. Our algorithms exploits overdispersion along with methods for learning sparse Poisson undirected graphical models for faster computation. We provide both theoretical guarantees and simulation results for both small and large-scale DAGs.

Wednesday December 9, 2015 19:00 - 23:59

210 C #52

210 C #52

Learning Theory and Algorithms for Forecasting Non-stationary Time Series
We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. We use our learning bounds to devise new algorithms for non-stationary time series forecasting for which we report some preliminary experimental results.

Wednesday December 9, 2015 19:00 - 23:59

210 C #95

210 C #95

Learning to Segment Object Candidates
Recent object detection systems rely on two critical steps: (1) a set of object proposals is predicted as efficiently as possible, and (2) this set of candidate proposals is then passed to an object classifier. Such approaches have been shown they can be fast, while achieving the state of the art in detection performance. In this paper, we propose a new way to generate object proposals, introducing an approach based on a discriminative convolutional network. Our model is trained jointly with two objectives: given an image patch, the first part of the system outputs a class-agnostic segmentation mask, while the second part of the system outputs the likelihood of the patch being centered on a full object. At test time, the model is efficiently applied on the whole test image and generates a set of segmentation masks, each of them being assigned with a corresponding object likelihood score. We show that our model yields significant improvements over state-of-the-art object proposal algorithms. In particular, compared to previous approaches, our model obtains substantially higher object recall using fewer proposals. We also show that our model is able to generalize to unseen categories it has not seen during training. Unlike all previous approaches for generating object masks, we do not rely on edges, superpixels, or any other form of low-level segmentation.

Wednesday December 9, 2015 19:00 - 23:59

210 C #8

210 C #8

Learning Wake-Sleep Recurrent Attention Models
Despite their success, convolutional neural networks are computationally expensive because they must examine all image locations. Stochastic attention-based models have been shown to improve computational efficiency at test time, but they remain difficult to train because of intractable posterior inference and high variance in the stochastic gradient estimates. Borrowing techniques from the literature on training deep generative models, we present the Wake-Sleep Recurrent Attention Model, a method for training stochastic attention networks which improves posterior inference and which reduces the variability in the stochastic gradients. We show that our method can greatly speed up the training time for stochastic attention networks in the domains of image classification and caption generation.

Wednesday December 9, 2015 19:00 - 23:59

210 C #14

210 C #14

Lifted Inference Rules With Constraints

Lifted inference rules exploit symmetries for fast reasoning in statistical rela-tional models. Computational complexity of these rules is highly dependent onthe choice of the constraint language they operate on and therefore coming upwith the right kind of representation is critical to the success of lifted inference.In this paper, we propose a new constraint language, called setineq, which allowssubset, equality and inequality constraints, to represent substitutions over the vari-ables in the theory. Our constraint formulation is strictly more expressive thanexisting representations, yet easy to operate on. We reformulate the three mainlifting rules: decomposer, generalized binomial and the recently proposed singleoccurrence for MAP inference, to work with our constraint representation. Exper-iments on benchmark MLNs for exact and sampling based inference demonstratethe effectiveness of our approach over several other existing techniques.

Wednesday December 9, 2015 19:00 - 23:59

210 C #56

210 C #56

Linear Multi-Resource Allocation with Semi-Bandit Feedback

We study an idealised sequential resource allocation problem. In each time step the learner chooses an allocation of several resource types between a number of tasks. Assigning more resources to a task increases the probability that it is completed. The problem is challenging because the alignment of the tasks to the resource types is unknown and the feedback is noisy. Our main contribution is the new setting and an algorithm with nearly-optimal regret analysis. Along the way we draw connections to the problem of minimising regret for stochastic linear bandits with heteroscedastic noise. We also present some new results for stochastic linear bandits on the hypercube that significantly out-performs existing work, especially in the sparse case.

Wednesday December 9, 2015 19:00 - 23:59

210 C #90

210 C #90

Local Smoothness in Variance Reduced Optimization

Abstract We propose a family of non-uniform sampling strategies to provably speed up a class of stochastic optimization algorithms with linear convergence including Stochastic Variance Reduced Gradient (SVRG) and Stochastic Dual Coordinate Ascent (SDCA). For a large family of penalized empirical risk minimization problems, our methods exploit data dependent local smoothness of the loss functions near the optimum, while maintaining convergence guarantees. Our bounds are the first to quantify the advantage gained from local smoothness which are significant for some problems significantly better. Empirically, we provide thorough numerical results to back up our theory. Additionally we present algorithms exploiting local smoothness in more aggressive ways, which perform even better in practice.

Wednesday December 9, 2015 19:00 - 23:59

210 C #72

210 C #72

Market Scoring Rules Act As Opinion Pools For Risk-Averse Agents
A market scoring rule (MSR) – a popular tool for designing algorithmic prediction markets – is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent’s risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents’ true probabilities. In particular, the logarithmic market scoring rule acts as a logarithmic pool for constant absolute risk aversion utility agents, and as a linear pool for an atypical budget-constrained agent utility with decreasing absolute risk aversion. We also point out the interpretation of a market maker under these conditions as a Bayesian learner even when agent beliefs are static.

Wednesday December 9, 2015 19:00 - 23:59

210 C #71

210 C #71

Matrix Completion Under Monotonic Single Index Models

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the challenge of matrix completion in the face of such nonlinearities. Given a few observations of a matrix that are obtained by applying a Lipschitz, monotonic function to a low rank matrix, our task is to estimate the remaining unobserved entries. We propose a novel matrix completion method that alternates between low-rank matrix estimation and monotonic function estimation to estimate the missing matrix elements. Mean squared error bounds provide insight into how well the matrix can be estimated based on the size, rank of the matrix and properties of the nonlinear transformation. Empirical results on synthetic and real-world datasets demonstrate the competitiveness of the proposed approach.

Wednesday December 9, 2015 19:00 - 23:59

210 C #75

210 C #75

Maximum Likelihood Learning With Arbitrary Treewidth via Fast-Mixing Parameter Sets

Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. This paper explores an alternative notion of a tractable set, namely a set of “fast-mixing parameters” where Markov chain Monte Carlo (MCMC) inference can be guaranteed to quickly converge to the stationary distribution. While it is common in practice to approximate the likelihood gradient using samples obtained from MCMC, such procedures lack theoretical guarantees. This paper proves that for any exponential family with bounded sufficient statistics, (not just graphical models) when parameters are constrained to a fast-mixing set, gradient descent with gradients approximated by sampling will approximate the maximum likelihood solution inside the set with high-probability. When unregularized, to find a solution epsilon-accurate in log-likelihood requires a total amount of effort cubic in 1/epsilon, disregarding logarithmic factors. When ridge-regularized, strong convexity allows a solution epsilon-accurate in parameter distance with an effort quadratic in 1/epsilon. Both of these provide of a fully-polynomial time randomized approximation scheme.

Wednesday December 9, 2015 19:00 - 23:59

210 C #65

210 C #65

MCMC for Variationally Sparse Gaussian Processes

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate covariance function parameter posteriors. This paper simultaneously addresses these, using a variational approximation to the posterior which is sparse in sup- port of the function but otherwise free-form. The result is a Hybrid Monte-Carlo sampling scheme which allows for a non-Gaussian approximation over the function values and covariance parameters simultaneously, with efficient computations based on inducing-point sparse GPs.

Wednesday December 9, 2015 19:00 - 23:59

210 C #30

210 C #30

Multi-Layer Feature Reduction for Tree Structured Group Lasso via Hierarchical Projection
Tree structured group Lasso (TGL) is a powerful technique in uncovering the tree structured sparsity over the features, where each node encodes a group of features. It has been applied successfully in many real-world applications. However, with extremely large feature dimensions, solving TGL remains a significant challenge due to its highly complicated regularizer. In this paper, we propose a novel Multi-Layer Feature reduction method (MLFre) to quickly identify the inactive nodes (the groups of features with zero coefficients in the solution) hierarchically in a top-down fashion, which are guaranteed to be irrelevant to the response. Thus, we can remove the detected nodes from the optimization without sacrificing accuracy. The major challenge in developing such testing rules is due to the overlaps between the parents and their children nodes. By a novel hierarchical projection algorithm, MLFre is able to test the nodes independently from any of their ancestor nodes. Moreover, we can integrate MLFre---that has a low computational cost---with any existing solvers. Experiments on both synthetic and real data sets demonstrate that the speedup gained by MLFre can be orders of magnitude.

Wednesday December 9, 2015 19:00 - 23:59

210 C #63

210 C #63

NEXT: A System for Real-World Development, Evaluation, and Application of Active Learning
Active learning methods automatically adapt data collection by selecting the most informative samples in order to accelerate machine learning. Because of this, real-world testing and comparing active learning algorithms requires collecting new datasets (adaptively), rather than simply applying algorithms to benchmark datasets, as is the norm in (passive) machine learning research. To facilitate the development, testing and deployment of active learning for real applications, we have built an open-source software system for large-scale active learning research and experimentation. The system, called NEXT, provides a unique platform for real-world, reproducible active learning research. This paper details the challenges of building the system and demonstrates its capabilities with several experiments. The results show how experimentation can help expose strengths and weaknesses of active learning algorithms, in sometimes unexpected and enlightening ways.

Wednesday December 9, 2015 19:00 - 23:59

210 C #28

210 C #28

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies.

Wednesday December 9, 2015 19:00 - 23:59

210 C #79

210 C #79

Nonparametric von Mises Estimators for Entropies, Divergences and Mutual Informations

We propose and analyse estimators for statistical functionals of one or moredistributions under nonparametric assumptions.Our estimators are derived from the von Mises expansion andare based on the theory of influence functions, which appearin the semiparametric statistics literature.We show that estimators based either on data-splitting or a leave-one-out techniqueenjoy fast rates of convergence and other favorable theoretical properties.We apply this framework to derive estimators for several popular informationtheoretic quantities, and via empirical evaluation, show the advantage of thisapproach over existing estimators.

Wednesday December 9, 2015 19:00 - 23:59

210 C #69

210 C #69

On the consistency theory of high dimensional variable screening

Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to produce the final model. The performance of variable screening depends on both computational efficiency and the ability to dramatically reduce the number of variables without discarding the important ones. When the data dimension $p$ is substantially larger than the sample size $n$, variable screening becomes crucial as 1) Faster feature selection algorithms are needed; 2) Conditions guaranteeing selection consistency might fail to hold.This article studies a class of linear screening methods and establishes consistency theory for this special class. In particular, we prove the restricted diagonally dominant (RDD) condition is a necessary and sufficient condition for strong screening consistency. As concrete examples, we show two screening methods $SIS$ and $HOLP$ are both strong screening consistent (subject to additional constraints) with large probability if $n > O((\rho s + \sigma/\tau)^2\log p)$ under random designs. In addition, we relate the RDD condition to the irrepresentable condition, and highlight limitations of $SIS$.

Wednesday December 9, 2015 19:00 - 23:59

210 C #92

210 C #92

On the Global Linear Convergence of Frank-Wolfe Optimization Variants

The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known to be slow (sublinear) when the solution lies at the boundary. A simple less-known fix is to add the possibility to take `away steps' during optimization, an operation that importantly does not require a feasibility oracle. In this paper, we highlight and clarify several variants of the Frank-Wolfe optimization algorithm that has been successfully applied in practice: FW with away steps, pairwise FW, fully-corrective FW and Wolfe's minimum norm point algorithm, and prove for the first time that they all enjoy global linear convergence under a weaker condition than strong convexity. The constant in the convergence rate has an elegant interpretation as the product of the (classical) condition number of the function with a novel geometric quantity that plays the role of the `condition number' of the constraint set. We provide pointers to where these algorithms have made a difference in practice, in particular with the flow polytope, the marginal polytope and the base polytope for submodular optimization.

Wednesday December 9, 2015 19:00 - 23:59

210 C #84

210 C #84

On-the-Job Learning with Bayesian Decision Theory
Our goal is to deploy a high-accuracy system starting with zero training examples. We consider an “on-the-job” setting, where as inputs arrive, we use real-time crowdsourcing to resolve uncertainty where needed and output our prediction when confident. As the model improves over time, the reliance on crowdsourcing queries decreases. We cast our setting as a stochastic game based on Bayesian decision theory, which allows us to balance latency, cost, and accuracy objectives in a principled way. Computing the optimal policy is intractable, so we develop an approximation based on Monte Carlo Tree Search. We tested our approach on three datasets-- named-entity recognition, sentiment classification, and image classification. On the NER task we obtained more than an order of magnitude reduction in cost compared to full human annotation, while boosting performance relative to the expert provided labels. We also achieve a 8% F1 improvement over having a single human label the whole set, and a 28% F1 improvement over online learning.

Wednesday December 9, 2015 19:00 - 23:59

210 C #15

210 C #15

Online Rank Elicitation for Plackett-Luce: A Dueling Bandits Approach

We study the problem of online rank elicitation, assuming that rankings of a set of alternatives obey the Plackett-Luce distribution. Following the setting of the dueling bandits problem, the learner is allowed to query pairwise comparisons between alternatives, i.e., to sample pairwise marginals of the distribution in an online fashion. Using this information, the learner seeks to reliably predict the most probable ranking (or top-alternative). Our approach is based on constructing a surrogate probability distribution over rankings based on a sorting procedure, for which the pairwise marginals provably coincide with the marginals of the Plackett-Luce distribution. In addition to a formal performance and complexity analysis, we present first experimental studies.

Wednesday December 9, 2015 19:00 - 23:59

210 C #60

210 C #60

Optimal Testing for Properties of Distributions
Given samples from an unknown distribution, p, is it possible to distinguish whether p belongs to some class of distributions C versus p being far from every distribution in C? This fundamental question has receivedtremendous attention in Statistics, albeit focusing onasymptotic analysis, as well as in Computer Science, wherethe emphasis has been on small sample size and computationalcomplexity. Nevertheless, even for basic classes ofdistributions such as monotone, log-concave, unimodal, and monotone hazard rate, the optimal sample complexity is unknown.We provide a general approach via which we obtain sample-optimal and computationally efficient testers for all these distribution families. At the core of our approach is an algorithm which solves the following problem:Given samplesfrom an unknown distribution p, and a known distribution q, are p and q close in Chi^2-distance, or far in total variation distance?The optimality of all testers is established by providing matching lower bounds. Finally, a necessary building block for our tester and important byproduct of our work are the first known computationally efficient proper learners for discretelog-concave and monotone hazard rate distributions. We exhibit the efficacy of our testers via experimental analysis.

Wednesday December 9, 2015 19:00 - 23:59

210 C #94

210 C #94

Optimization Monte Carlo: Efficient and Embarrassingly Parallel Likelihood-Free Inference

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a vector of random numbers u, in such a way that the outcome, knowing u, is deterministic. For each instantiation of u we run an optimization procedure to minimize the distance between summary statistics of the simulator and the data. After reweighing these samples using the prior and the Jacobian (accounting for the change of volume in transforming from the space of summary statistics to the space of parameters) we show that this weighted ensemble represents a Monte Carlo estimate of the posterior distribution. The procedure can be run embarrassingly parallel (each node handling one sample) and anytime (by allocating resources to the worst performing sample). The procedure is validated on six experiments.

Wednesday December 9, 2015 19:00 - 23:59

210 C #37

210 C #37

Pointer Networks
We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that arediscrete tokens corresponding to positions in an input sequence.Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines,because the number of target classes in eachstep of the output depends on the length of the input, which is variable.Problems such as sorting variable sized sequences, and various combinatorialoptimization problems belong to this class. Our model solvesthe problem of variable size output dictionaries using a recently proposedmechanism of neural attention. It differs from the previous attentionattempts in that, instead of using attention to blend hidden units of anencoder to a context vector at each decoder step, it uses attention asa pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net).We show Ptr-Nets can be used to learn approximate solutions to threechallenging geometric problems -- finding planar convex hulls, computingDelaunay triangulations, and the planar Travelling Salesman Problem-- using training examples alone. Ptr-Nets not only improve oversequence-to-sequence with input attention, butalso allow us to generalize to variable size output dictionaries.We show that the learnt models generalize beyond the maximum lengthsthey were trained on. We hope our results on these taskswill encourage a broader exploration of neural learning for discreteproblems.

Wednesday December 9, 2015 19:00 - 23:59

210 C #22

210 C #22

Policy Gradient for Coherent Risk Measures

Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as the variance or conditional value at risk (CVaR). In this work, we extend the policy gradient method to the whole class of coherent risk measures, which is widely accepted in finance and operations research, among other fields. We consider both static and time-consistent dynamic risk measures. For static risk measures, our approach is in the spirit of policy gradient algorithms and combines a standard sampling approach with convex programming. For dynamic risk measures, our approach is actor-critic style and involves explicit approximation of value function. Most importantly, our contribution presents a unified approach to risk-sensitive reinforcement learning that generalizes and extends previous results.

Wednesday December 9, 2015 19:00 - 23:59

210 C #82

210 C #82

Practical and Optimal LSH for Angular Distance

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH (Andoni-Indyk-Nguyen-Razenshteyn 2014) (Andoni-Razenshteyn 2015)), our algorithm is also practical, improving upon the well-studied hyperplane LSH (Charikar 2002) in practice. We also introduce a multiprobe version of this algorithm and conduct an experimental evaluation on real and synthetic data sets.We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

Wednesday December 9, 2015 19:00 - 23:59

210 C #49

210 C #49

Precision-Recall-Gain Curves: PR Analysis Done Right
Precision-Recall analysis abounds in applications of binary classification where true negatives do not add value and hence should not affect assessment of the classifier's performance. Perhaps inspired by the many advantages of receiver operating characteristic (ROC) curves and the area under such curves for accuracy-based performance assessment, many researchers have taken to report Precision-Recall (PR) curves and associated areas as performance metric. We demonstrate in this paper that this practice is fraught with difficulties, mainly because of incoherent scale assumptions -- e.g., the area under a PR curve takes the arithmetic mean of precision values whereas the $F_{\beta}$ score applies the harmonic mean. We show how to fix this by plotting PR curves in a different coordinate system, and demonstrate that the new Precision-Recall-Gain curves inherit all key advantages of ROC curves. In particular, the area under Precision-Recall-Gain curves conveys an expected $F_1$ score on a harmonic scale, and the convex hull of a Precision-Recall-Gain curve allows us to calibrate the classifier's scores so as to determine, for each operating point on the convex hull, the interval of $\beta$ values for which the point optimises $F_{\beta}$. We demonstrate experimentally that the area under traditional PR curves can easily favour models with lower expected $F_1$ score than others, and so the use of Precision-Recall-Gain curves will result in better model selection.

Wednesday December 9, 2015 19:00 - 23:59

210 C #25

210 C #25

Principal Differences Analysis: Interpretable Characterization of Differences between Distributions

We introduce principal differences analysis for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate populations. Relying on the Cramer-Wold device, it requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class differences. A sparse variant of the method is introduced to identify features responsible for the differences. We provide algorithms for both the original minimax formulation as well as its semidefinite relaxation. In addition to deriving some convergence results, we illustrate how the approach may be applied to identify differences between cell populations in the somatosensory cortex and hippocampus as manifested by single cell RNA-seq. Our broader framework extends beyond the specific choice of Wasserstein divergence.

Wednesday December 9, 2015 19:00 - 23:59

210 C #50

210 C #50

Quartz: Randomized Dual Coordinate Ascent with Arbitrary Sampling

We study the problem of minimizing the average of a large number of smooth convex functions penalized with a strongly convex regularizer. We propose and analyze a novel primal-dual method (Quartz) which at every iteration samples and updates a random subset of the dual variables, chosen according to an arbitrary distribution. In contrast to typical analysis, we directly bound the decrease of the primal-dual error (in expectation), without the need to first analyze the dual error. Depending on the choice of the sampling, we obtain efficient serial and mini-batch variants of the method. In the serial case, our bounds match the best known bounds for SDCA (both with uniform and importance sampling). With standard mini-batching, our bounds predict initial data-independent speedup as well as additional data-driven speedup which depends on spectral and sparsity properties of the data.

Wednesday December 9, 2015 19:00 - 23:59

210 C #85

210 C #85

Recovering Communities in the General Stochastic Block Model Without Knowing the Parameters

The stochastic block model (SBM) has recently gathered significant attention due to new threshold phenomena. However, most developments rely on the knowledge of the model parameters, or at least on the number of communities. This paper introduces efficient algorithms that do not require such knowledge and yet achieve the optimal information-theoretic tradeoffs identified in Abbe-Sandon '15. In the constant degree regime, an algorithm is developed that requires only a lower-bound on the relative sizes of the communities and achieves the optimal accuracy scaling for large degrees. This lower-bound requirement is removed for the regime of diverging degrees. For the logarithmic degree regime, this is further enhanced into a fully agnostic algorithm that simultaneously learns the model parameters, achieves the optimal CH-limit for exact recovery, and runs in quasi-linear time. These provide the first algorithms affording efficiency, universality and information-theoretic optimality for strong and weak consistency in the SBM.

Wednesday December 9, 2015 19:00 - 23:59

210 C #64

210 C #64

Regret-Based Pruning in Extensive-Form Games

Counterfactual Regret Minimization (CFR) is a leading algorithm for finding a Nash equilibrium in large zero-sum imperfect-information games. CFR is an iterative algorithm that repeatedly traverses the game tree, updating regrets at each information set.We introduce an improvement to CFR that prunes any path of play in the tree, and its descendants, that has negative regret. It revisits that sequence at the earliest subsequent CFR iteration where the regret could have become positive, had that path been explored on every iteration. The new algorithm maintains CFR's convergence guarantees while making iterations significantly faster---even if previously known pruning techniques are used in the comparison. This improvement carries over to CFR+, a recent variant of CFR. Experiments show an order of magnitude speed improvement, and the relative speed improvement increases with the size of the game.

Wednesday December 9, 2015 19:00 - 23:59

210 C #68

210 C #68

Segregated Graphs and Marginals of Chain Graph Models

Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) generalizes both Bayesian networks and MRFs, and can represent asymmetric and symmetric relationships together.As in other graphical models, the set of marginals from distributions in a chain graph model induced by the presence of hidden variables forms a complex model. One recent approach to the study of marginal graphical models is to consider a well-behaved supermodel. Such a supermodel of marginals of Bayesian networks, defined only by conditional independences, and termed the ordinary Markov model, was studied at length in (Evans and Richardson, 2014).In this paper, we show that special mixed graphs which we call segregated graphs can be associated, via a Markov property, with supermodels of a marginal of chain graphs defined only by conditional independences. Special features of segregated graphs imply the existence of a very natural factorization for these supermodels, and imply many existing results on the chain graph model, and ordinary Markov model carry over. Our results suggest that segregated graphs define an analogue of the ordinary Markov model for marginals of chain graph models.

Wednesday December 9, 2015 19:00 - 23:59

210 C #61

210 C #61

Semi-supervised Convolutional Neural Networks for Text Categorization via Region Embedding
This paper presents a new semi-supervised framework with convolutional neural networks (CNNs) for text categorization. Unlike the previous approaches that rely on word embeddings, our method learns embeddings of small text regions from unlabeled data for integration into a supervised CNN. The proposed scheme for embedding learning is based on the idea of two-view semi-supervised learning, which is intended to be useful for the task of interest even though the training is done on unlabeled data. Our models achieve better results than previous approaches on sentiment classification and topic classification tasks.

Wednesday December 9, 2015 19:00 - 23:59

210 C #11

210 C #11

Softstar: Heuristic-Guided Probabilistic Inference

Recent machine learning methods for sequential behavior prediction estimate the motives of behavior rather than the behavior itself. This higher-level abstraction improves generalization in different prediction settings, but computing predictions often becomes intractable in large decision spaces. We propose the Softstar algorithm, a softened heuristic-guided search technique for the maximum entropy inverse optimal control model of sequential behavior. This approach supports probabilistic search with bounded approximation error at a significantly reduced computational cost when compared to sampling based methods. We present the algorithm, analyze approximation guarantees, and compare performance with simulation-based inference on two distinct complex decision tasks.

Wednesday December 9, 2015 19:00 - 23:59

210 C #45

210 C #45

Sparse Linear Programming via Primal and Dual Augmented Coordinate Descent

Over the past decades, Linear Programming (LP) has been widely used in different areas and considered as one of the mature technologies in numerical optimization. However, the complexity offered by state-of-the-art algorithms (i.e. interior-point method and primal, dual simplex methods) is still unsatisfactory for problems in machine learning with huge number of variables and constraints. In this paper, we investigate a general LP algorithm based on the combination of Augmented Lagrangian and Coordinate Descent (AL-CD), giving an iteration complexity of $O((\log(1/\epsilon))^2)$ with $O(nnz(A))$ cost per iteration, where $nnz(A)$ is the number of non-zeros in the $m\times n$ constraint matrix $A$, and in practice, one can further reduce cost per iteration to the order of non-zeros in columns (rows) corresponding to the active primal (dual) variables through an active-set strategy. The algorithm thus yields a tractable alternative to standard LP methods for large-scale problems of sparse solutions and $nnz(A)\ll mn$. We conduct experiments on large-scale LP instances from $\ell_1$-regularized multi-class SVM, Sparse Inverse Covariance Estimation, and Nonnegative Matrix Factorization, where the proposed approach finds solutions of $10^{-3}$ precision orders of magnitude faster than state-of-the-art implementations of interior-point and simplex methods.

Wednesday December 9, 2015 19:00 - 23:59

210 C #76

210 C #76

Sparse PCA via Bipartite Matchings

We consider the following multi-component sparse PCA problem:given a set of data points, we seek to extract a small number of sparse components with \emph{disjoint} supports that jointly capture the maximum possible variance.Such components can be computed one by one, repeatedly solving the single-component problem and deflating the input data matrix, but this greedy procedure is suboptimal.We present a novel algorithm for sparse PCA that jointly optimizes multiple disjoint components. The extracted features capture variance that lies within a multiplicative factor arbitrarily close to $1$ from the optimal.Our algorithm is combinatorial and computes the desired components by solving multiple instances of the bipartite maximum weight matching problem.Its complexity grows as a low order polynomial in the ambient dimension of the input data, but exponentially in its rank.However, it can be effectively applied on a low-dimensional sketch of the input data.We evaluate our algorithm on real datasets and empirically demonstrate that in many cases it outperforms existing, deflation-based approaches.

Wednesday December 9, 2015 19:00 - 23:59

210 C #57

210 C #57

Spatial Transformer Networks
Convolutional Neural Networks define an exceptionallypowerful class of model, but are still limited by the lack of abilityto be spatially invariant to the input data in a computationally and parameterefficient manner. In this work we introduce a new learnable module, theSpatial Transformer, which explicitly allows the spatial manipulation ofdata within the network. This differentiable module can be insertedinto existing convolutional architectures, giving neural networks the ability toactively spatially transform feature maps, conditional on the feature map itself,without any extra training supervision or modification to the optimisation process. We show that the useof spatial transformers results in models which learn invariance to translation,scale, rotation and more generic warping, resulting in state-of-the-artperformance on several benchmarks, and for a numberof classes of transformations.

Wednesday December 9, 2015 19:00 - 23:59

210 C #3

210 C #3

Spectral Learning of Large Structured HMMs for Comparative Epigenomics

We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure. The main challenge with learning parameters of such models is that iterative methods such as EM are very slow, while naive spectral methods result in time and space complexity exponential in the number of cell types. We exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets. We provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types. Finally, we show that beyond our specific model, some of our algorithmic ideas can be applied to other graphical models.

Wednesday December 9, 2015 19:00 - 23:59

210 C #35

210 C #35

Statistical Topological Data Analysis - A Kernel Perspective

We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel which would enable a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in two-sample hypothesis testing on synthetic as well as real-world data.

Wednesday December 9, 2015 19:00 - 23:59

210 C #43

210 C #43

Stochastic Online Greedy Learning with Semi-bandit Feedbacks

The greedy algorithm is extensively studied in the field of combinatorial optimization for decades. In this paper, we address the online learning problem when the input to the greedy algorithm is stochastic with unknown parameters that have to be learned over time. We first propose the greedy regret and $\epsilon$-quasi greedy regret as learning metrics comparing with the performance of offline greedy algorithm. We then propose two online greedy learning algorithms with semi-bandit feedbacks, which use multi-armed bandit and pure exploration bandit policies at each level of greedy learning, one for each of the regret metrics respectively. Both algorithms achieve $O(\log T)$ problem-dependent regret bound ($T$ being the time horizon) for a general class of combinatorial structures and reward functions that allow greedy solutions. We further show that the bound is tight in $T$ and other problem instance parameters.

Wednesday December 9, 2015 19:00 - 23:59

210 C #89

210 C #89

Streaming Min-max Hypergraph Partitioning

In many applications, the data is of rich structure that can be represented by a hypergraph, where the data items are represented by vertices and the associations among items are represented by hyperedges. Equivalently, we are given an input bipartite graph with two types of vertices: items, and associations (which we refer to as topics). We consider the problem of partitioning the set of items into a given number of parts such that the maximum number of topics covered by a part of the partition is minimized. This is a natural clustering problem, with various applications, e.g. partitioning of a set of information objects such as documents, images, and videos, and load balancing in the context of computation platforms.In this paper, we focus on the streaming computation model for this problem, in which items arrive online one at a time and each item must be assigned irrevocably to a part of the partition at its arrival time. Motivated by scalability requirements, we focus on the class of streaming computation algorithms with memory limited to be at most linear in the number of the parts of the partition. We show that a greedy assignment strategy is able to recover a hidden co-clustering of items under a natural set of recovery conditions. We also report results of an extensive empirical evaluation, which demonstrate that this greedy strategy yields superior performance when compared with alternative approaches.

Wednesday December 9, 2015 19:00 - 23:59

210 C #53

210 C #53

Streaming, Distributed Variational Inference for Bayesian Nonparametrics

This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational posterior for each, and make asynchronous streaming updates to a central model. In contrast to previous algorithms, the proposed framework is truly streaming, distributed, asynchronous, learning-rate-free, and truncation-free. The key challenge in developing the framework, arising from fact that BNP models do not impose an inherent ordering on their components, is finding the correspondence between minibatch and central BNP posterior components before performing each update. To address this, the paper develops a combinatorial optimization problem over component correspondences, and provides an efficient solution technique. The paper concludes with an application of the methodology to the DP mixture model, with experimental results demonstrating its practical scalability and performance.

Wednesday December 9, 2015 19:00 - 23:59

210 C #31

210 C #31

Structured Transforms for Small-Footprint Deep Learning
We consider the task of building compact deep learning pipelines suitable for deploymenton storage and power constrained mobile devices. We propose a uni-fied framework to learn a broad family of structured parameter matrices that arecharacterized by the notion of low displacement rank. Our structured transformsadmit fast function and gradient evaluation, and span a rich range of parametersharing configurations whose statistical modeling capacity can be explicitly tunedalong a continuum from structured to unstructured. Experimental results showthat these transforms can significantly accelerate inference and forward/backwardpasses during training, and offer superior accuracy-compactness-speed tradeoffsin comparison to a number of existing techniques. In keyword spotting applicationsin mobile speech recognition, our methods are much more effective thanstandard linear low-rank bottleneck layers and nearly retain the performance ofstate of the art models, while providing more than 3.5-fold compression.

Wednesday December 9, 2015 19:00 - 23:59

210 C #34

210 C #34

Testing Closeness With Unequal Sized Samples

We consider the problem of testing whether two unequal-sized samples were drawn from identical distributions, versus distributions that differ significantly. Specifically, given a target error parameter $\eps > 0$, $m_1$ independent draws from an unknown distribution $p$ with discrete support, and $m_2$ draws from an unknown distribution $q$ of discrete support, we describe a test for distinguishing the case that $p=q$ from the case that $||p-q||_1 \geq \eps$. If $p$ and $q$ are supported on at most $n$ elements, then our test is successful with high probability provided $m_1\geq n^{2/3}/\varepsilon^{4/3}$ and $m_2 = \Omega\left(\max\{\frac{n}{\sqrt m_1\varepsilon^2}, \frac{\sqrt n}{\varepsilon^2}\}\right).$ We show that this tradeoff is information theoretically optimal throughout this range, in the dependencies on all parameters, $n,m_1,$ and $\eps$, to constant factors. As a consequence, we obtain an algorithm for estimating the mixing time of a Markov chain on $n$ states up to a $\log n$ factor that uses $\tilde{O}(n^{3/2} \tau_{mix})$ queries to a ``next node'' oracle. The core of our testing algorithm is a relatively simple statistic that seems to perform well in practice, both on synthetic data and on natural language data. We believe that this statistic might prove to be a useful primitive within larger machine learning and natural language processing systems.

Wednesday December 9, 2015 19:00 - 23:59

210 C #66

210 C #66

The Return of the Gating Network: Combining Generative Models and Discriminative Training in Natural Image Priors
In recent years, approaches based on machine learning have achieved state-of-the-art performance on image restoration problems. Successful approaches include both generative models of natural images as well as discriminative training of deep neural networks. Discriminative training of feed forward architectures allows explicit control over the computational cost of performing restoration and therefore often leads to better performance at the same cost at run time. In contrast, generative models have the advantage that they can be trained once and then adapted to any image restoration task by a simple use of Bayes' rule. In this paper we show how to combine the strengths of both approaches by training a discriminative, feed-forward architecture to predict the state of latent variables in a generative model of natural images. We apply this idea to the very successful Gaussian Mixture Model (GMM) of natural images. We show that it is possible to achieve comparable performance as the original GMM but with two orders of magnitude improvement in run time while maintaining the advantage of generative models.

Wednesday December 9, 2015 19:00 - 23:59

210 C #12

210 C #12

Training Very Deep Networks
Theoretical and empirical evidence indicates that the depth of neural networks is crucial for their success. However, training becomes more difficult as depth increases, and training of very deep networks remains an open problem. Here we introduce a new architecture designed to overcome this. Our so-called highway networks allow unimpeded information flow across many layers on information highways. They are inspired by Long Short-Term Memory recurrent networks and use adaptive gating units to regulate the information flow. Even with hundreds of layers, highway networks can be trained directly through simple gradient descent. This enables the study of extremely deep and efficient architectures.

Wednesday December 9, 2015 19:00 - 23:59

210 C #4

210 C #4

Variance Reduced Stochastic Gradient Descent with Neighbors

Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet it is also known to be slow relative to steepest descent. Recently, variance reduction techniques such as SVRG and SAGA have been proposed to overcome this weakness. With asymptotically vanishing variance, a constant step size can be maintained, resulting in geometric convergence rates. However, these methods are either based on occasional computations of full gradients at pivot points (SVRG), or on keeping per data point corrections in memory (SAGA). This has the disadvantage that one cannot employ these methods in a streaming setting and that speed-ups relative to SGD may need a certain number of epochs in order to materialize. This paper investigates a new class of algorithms that can exploit neighborhood structure in the training data to share and re-use information about past stochastic gradients across data points. While not meant to be offering advantages in an asymptotic setting, there are significant benefits in the transient optimization phase, in particular in a streaming or single-epoch setting. We investigate this family of algorithms in a thorough analysis and show supporting experimental results. As a side-product we provide a simple and unified proof technique for a broad class of variance reduction algorithms.

Wednesday December 9, 2015 19:00 - 23:59

210 C #78

210 C #78

Variational Consensus Monte Carlo

Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large datasets typical of modern machine learning. The recently proposed consensus Monte Carlo algorithm removes this limitation by partitioning the data and drawing samples conditional on each partition in parallel (Scott et al, 2013). A fixed aggregation function then combines these samples, yielding approximate posterior samples. We introduce variational consensus Monte Carlo (VCMC), a variational Bayes algorithm that optimizes over aggregation functions to obtain samples from a distribution that better approximates the target. The resulting objective contains an intractable entropy term; we therefore derive a relaxation of the objective and show that the relaxed problem is blockwise concave under mild conditions. We illustrate the advantages of our algorithm on three inference tasks from the literature, demonstrating both the superior quality of the posterior approximation and the moderate overhead of the optimization step. Our algorithm achieves a relative error reduction (measured against serial MCMC) of up to 39% compared to consensus Monte Carlo on the task of estimating 300-dimensional probit regression parameter expectations; similarly, it achieves an error reduction of 92% on the task of estimating cluster comembership probabilities in a Gaussian mixture model with 8 components in 8 dimensions. Furthermore, these gains come at moderate cost compared to the runtime of serial MCMC, achieving near-ideal speedup in some instances.

Wednesday December 9, 2015 19:00 - 23:59

210 C #44

210 C #44

Weighted Theta Functions and Embeddings with Applications to Max-Cut, Clustering and Summarization

**Speakers**
## Prof Chiranjib Bhattacharyya

We introduce a unifying generalization of the Lovász theta function, and the associated geometric embedding, for graphs with weights on both nodes and edges. We show how it can be computed exactly by semidefinite programming, and how to approximate it using SVM computations. We show how the theta function can be interpreted as a measure of diversity in graphs and use this idea, and the graph embedding in algorithms for Max-Cut, correlation clustering and document summarization, all of which are well represented as problems on weighted graphs.

Professor Dept of Comp. Science & Automation, Indian Institute of Science - Bangalore

Chiranjib Bhattacharyya is currently Professor in the Department of Computer Science and Automation, Indian Institute of Science. His research interests are in Machine Learning, Optimisation and their applications to Industrial problems. He joined the Department of CSA, IISc, in 2002 as an Assistant Professor. Prior to joining the Department he was a postdoctoral fellow at UC Berkeley. He holds BE and ME degrees, both in Electrical... Read More →

Wednesday December 9, 2015 19:00 - 23:59

210 C #59

210 C #59

When are Kalman-Filter Restless Bandits Indexable?

We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is {\it indexable} in the sense that the {\it Whittle index} is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, this appears to be the first such proof. We use results about {\it Schur-convexity} and {\it mechanical words}, which are particularbinary strings intimately related to {\it palindromes}.

Wednesday December 9, 2015 19:00 - 23:59

210 C #81

210 C #81

Where are they looking?
Humans have the remarkable ability to follow the gaze of other people to identify what they are looking at. Following eye gaze, or gaze-following, is an important ability that allows us to understand what other people are thinking, the actions they are performing, and even predict what they might do next. Despite the importance of this topic, this problem has only been studied in limited scenarios within the computer vision community. In this paper, we propose a deep neural network-based approach for gaze-following and a new benchmark dataset for thorough evaluation. Given an image and the location of a head, our approach follows the gaze of the person and identifies the object being looked at. After training, the network is able to discover how to extract head pose and gaze orientation, and to select objects in the scene that are in the predicted line of sight and likely to be looked at (such as televisions, balls and food). The quantitative evaluation shows that our approach produces reliable results, even when viewing only the back of the head. While our method outperforms several baseline approaches, we are still far from reaching human performance at this task. Overall, we believe that this is a challenging and important task that deserves more attention from the community.

Wednesday December 9, 2015 19:00 - 23:59

210 C #2

210 C #2

Learning with Intelligent Teacher: Similarity Control and Knowledge Transfer

In the talk, I will introduce a model of learning with Intelligent Teacher. In this model, Intelligent Teacher

supplies (some) training examples $\mathscr{(x_i, y_i), i=1, \dots , l, x_i \in X,y_i \in \{-1,1\}}$ with additional

(privileged) information) $\mathscr{x_i^* \in X^*}$ forming training triplets $\mathscr (x_i,x_i^*, y_i), i, \dots ,

l$. Privileged information is available only for training examples and $not\, available\, for\, text\, examples$.

Using privileged information it is required to find a better training processes (that use less examples or more

accurate with the same number of examples) than the classical ones.

In this lecture, I will present two additional mechanisms that exist in learning with Intelligent Teacher

* The mechanism to control Student's concept of examples similarity and

* The mechanism to transfer knowledge that can be obtained in space of privileged information to the desired space of decision rules.

Privileged information exists for many inference problem and Student-Teacher interaction can be considered as the basic element of intelligent behavior.

supplies (some) training examples $\mathscr{(x_i, y_i), i=1, \dots , l, x_i \in X,y_i \in \{-1,1\}}$ with additional

(privileged) information) $\mathscr{x_i^* \in X^*}$ forming training triplets $\mathscr (x_i,x_i^*, y_i), i, \dots ,

l$. Privileged information is available only for training examples and $not\, available\, for\, text\, examples$.

Using privileged information it is required to find a better training processes (that use less examples or more

accurate with the same number of examples) than the classical ones.

In this lecture, I will present two additional mechanisms that exist in learning with Intelligent Teacher

* The mechanism to control Student's concept of examples similarity and

* The mechanism to transfer knowledge that can be obtained in space of privileged information to the desired space of decision rules.

Privileged information exists for many inference problem and Student-Teacher interaction can be considered as the basic element of intelligent behavior.

Thursday Dec