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.

翻译：本文研究线性回归系数的鲁棒估计问题。本工作重点关注以下情形：协变量采样自协方差未知的$L$-次高斯分布，噪声采样自具有有界绝对矩的分布，且协变量与噪声均可能受到对抗性污染。我们推导出估计误差界，该误差界依赖于协变量协方差矩阵的稳定秩与条件数，且估计过程具有多项式计算复杂度。