Robust Mean Estimation in High Dimensions via _0 Minimization

Abstract

We study the robust mean estimation problem in high dimensions, where <0.5 fraction of the data points can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the minimization of the _0-`norm' of the outlier indicator vector, under second moment constraints on the inlier data points. We prove that the global minimum of this objective is order optimal for the robust mean estimation problem, and we propose a general framework for minimizing the objective. We further leverage the _1 and _p (0<p<1), minimization techniques in compressive sensing to provide computationally tractable solutions to the _0 minimization problem. Both synthetic and real data experiments demonstrate that the proposed algorithms significantly outperform state-of-the-art robust mean estimation methods.

Tasks

Reproductions