Adversarial robust weighted Huber regression
This work addresses robust regression for scenarios with adversarial data corruption, but it appears incremental as it builds on existing robust estimation frameworks.
The paper tackles robust linear regression with adversarial contamination in covariates and noise, deriving an estimation error bound that depends on the stable rank and condition number of the covariance matrix, with polynomial computational complexity.
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.