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Activity Number: 626 - Recent Advances in High-Dimensional Statistical Inference
Type: Invited
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #300060 Presentation
Title: Robust Statistics Meets Nonconvex Optimization
Author(s): Wenxin Zhou* and Qiang Sun
Companies: University of California, San Diego and University of Toronto
Keywords: Robust statistics; Nonconvex optimization; Oracle property; Heavy-tailed; Sparse regression

We propose a computational framework to simultaneously control statistical error and algorithmic complexity when fitting sparse regression models with heavy-tailed and/or asymmetric errors. Statistically, we show that if the loss function is carefully calibrated to fit the noise level and the intrinsic structure of the model, the ill-effects of outliers caused by the noise can be removed, or at least dampened. Computationally, we propose a two-stage (contraction and tightening) procedure with controlled algorithmic complexity. The first stage solves a convex problem to obtain a coarse initial estimator, which is further refined in the second stage by iteratively solving a sequence of convex programs. Theoretically we show that the resulting estimator from our algorithm achieves the optimal rate of convergence and oracle properties.

Authors who are presenting talks have a * after their name.

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