Adversarial robust weighted Huber regression

TL;DR

This paper develops a robust method for linear regression that withstands adversarial contamination, using weighted Huber regression and providing error bounds based on covariance properties.

Contribution

It introduces a novel robust weighted Huber regression approach for adversarially contaminated data with theoretical error bounds.

Findings

Estimation error depends on stable rank and condition number of covariance matrix.

Method handles adversarial contamination in covariates and noise.

Polynomial computational complexity for estimation.

Abstract

We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution with a bounded absolute moment and both covariates and noises may be contaminated by an adversary. We derive an estimation error bound, which depends on the stable rank and the condition number of the covariance matrix of covariates with a polynomial computational complexity of estimation.