Year: 2020
Type: preprint
Abstract: We study the robust mean estimation problem in high dimensions, where $α<0.5$ 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 $\ell_0$-`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 $\ell_1$ and $\ell_p$ $(0
Source: arXiv (Cornell University)
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3081284428