Adversarial robust weighted Huber regression
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.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Robust regression with covariate filtering: Heavy tails and adversarial contamination
We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated. Several computationally efficient estimators have been proposed for the …
regressionA Statistical Learning Assessment of Huber Regression
As one of the triumphs and milestones of robust statistics, Huber regression plays an important role in robust inference and estimation. It has also been finding a great variety of applications in machine learning. In a …
regressionRobust Nonparametric Regression under Huber's $ε$-contamination Model
We consider the non-parametric regression problem under Huber's $\epsilon$-contamination model, in which an $\epsilon$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple loca…
modelregressionIteratively Reweighted $\ell_1$-Penalized Robust Regression
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 …
regressionVariable SelectionOnline and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination
In this work we revisit two classic high-dimensional online learning problems, namely linear regression and contextual bandits, from the perspective of adversarial robustness. Existing works in algorithmic robust statist…
Adversarial RobustnessMulti-Armed Banditsregression