Iteratively Reweighted _1-Penalized Robust Regression

Code

• github.com/XiaoouPan/ILAMM
  OfficialIn papertf★ 0
• github.com/XiaoouPan/tfHuber
  none★ 0

Abstract

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moment, we show that iteratively reweighted _1-penalized adaptive Huber regression estimator satisfies exponential deviation bounds and oracle properties, including the oracle convergence rate and variable selection consistency, under a weak beta-min condition. Computationally, we need as many as O( s + d) iterations to reach such an oracle estimator, where s and d denote the sparsity and ambient dimension, respectively. Extension to a general class of robust loss functions is also considered. Numerical studies lend strong support to our methodology and theory.

Tasks

Reproductions