Adaptive Robustness and Sub-Gaussian Deviations in Sparse Linear Regression - Probability and Statistics Seminar

Explore robust estimation in sparse linear regression with this 49-minute USC Probability and Statistics Seminar talk. Delve into the framework of robust estimation for outliers and heavy-tailed noise, focusing on the sparse linear model with corrupted observations. Learn about the minimax quadratic risk for signal estimation and discover a novel, fully adaptive procedure that achieves optimality. Examine the penalized pivotal estimation problem and its resulting method, which offers minimax optimality, robustness, and sub-Gaussian deviations even with heavy-tailed noise. Cover topics including estimating the mean, confidence bounds under two moments, robust procedures, adversarial contamination, oblivious corruption, lower bounds, and the Pivotal Double SLOPE method. Gain insights from this joint work by Simo Ndaoud, S. Minsker, and L. Wang, presented at ESSEC.