An Optimal Aggregation Procedure For Nonparametric Regression With Convex And Non-convex Models

Series: 
Stochastics Seminar
Thursday, November 3, 2016 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
University of Pennsylvania, Department of Statistics, The Wharton School
Organizer: 
Exact oracle inequalities for regression have been extensively studied in statistics and learning theory over the past decade. In the case of a misspecified model, the focus has been on either parametric or convex classes. We present a new estimator that steps outside of the model in the non-convex case and reduces to least squares in the convex case. To analyze the estimator for general non-parametric classes, we prove a generalized Pythagorean theorem and study the supremum of a negative-mean stochastic process (which we term the offset Rademacher complexity) via the chaining technique.(joint work with T. Liang and K. Sridharan)