Philip Thompson

Outlier-robust estimation of a sparse linear model using $\ell_1$-penalized Huber's $M$-estimator

We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the $\ell_1$-penalized Huber's $M$-estimator based on $n$ samples attains the optimal r…