  We propose a novel method to estimate the coefficients of linear regression
when outputs and inputs are contaminated by malicious outliers. Our method
consists of two-step: (i) Make appropriate weights
$\left\{\hat{w}_i\right\}_{i=1}^n$ such that the weighted sample mean of
regression covariates robustly estimates the population mean of the regression
covariate, (ii) Process Huber regression using
$\left\{\hat{w}_i\right\}_{i=1}^n$. When (a) the regression covariate is a
sequence with i.i.d. random vectors drawn from sub-Gaussian distribution with
unknown mean and known identity covariance and (b) the absolute moment of the
random noise is finite, our method attains a faster convergence rate than
Diakonikolas, Kong and Stewart (2019) and Cherapanamjeri et al. (2020).
Furthermore, our result is minimax optimal up to constant factor. When (a) the
regression covariate is a sequence with i.i.d. random vectors drawn from heavy
tailed distribution with unknown mean and bounded kurtosis and (b) the absolute
moment of the random noise is finite, our method attains a convergence rate,
which is minimax optimal up to constant factor.
