Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates

TL;DR

This paper introduces a robust, efficient, and nearly optimal method for estimating linear regression coefficients in the presence of heavy-tailed noises, covariates, and malicious outliers.

Contribution

It proposes a new estimator that handles heavy-tailed distributions and outliers effectively, with computational efficiency and near-optimal error bounds.

Findings

Estimator is computationally efficient.

Error bounds are nearly optimal.

Effective against heavy-tailed noises and outliers.

Abstract

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are contaminated by malicious outliers. Our estimator can be computed efficiently. Further, the error bound of the estimator is nearly optimal.