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

Stochastics Seminar
Thursday, November 3, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 006
University of Pennsylvania, Department of Statistics, The Wharton School
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)