Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliers

TL;DR

This paper addresses sparse linear regression with heavy-tailed and contaminated data, proposing efficient estimators with sharp error bounds for challenging real-world scenarios.

Contribution

It introduces robust estimators for sparse linear regression that handle heavy-tailed distributions and outliers, with proven efficiency and accuracy.

Findings

Estimators are computationally efficient.

Achieve sharp error bounds under heavy-tailed contamination.

Handle both heavy tails and outliers effectively.

Abstract

We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and noises are sampled from heavy tailed distributions but also contaminated by outliers. Our estimators can be computed efficiently, and exhibit sharp error bounds.