Robust Regression under Adversarial Contamination: Theory and Algorithms for the Welsch Estimator
对抗污染下的稳健回归:Welsch 估计量的理论与算法
Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex M-estimator, specifically the Welsch estimator, and show that it can eliminate this bias whenever it is statistically identifiable. We focus on high-dimensional linear regression under adversarial contamination, where a fraction of samples may…