This event has ended. View the official site or create your own event → Check it out
This event has ended. Create your own
View analytic
Wednesday, December 9 • 19:00 - 23:59
Beyond Sub-Gaussian Measurements: High-Dimensional Structured Estimation with Sub-Exponential Designs

Sign up or log in to save this to your schedule and see who's attending!

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