Robust Principal Component Analysis with Non-Sparse Errors

Jushan Bai and Junlong Feng

Papers from arXiv.org

Abstract: We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a new theoretical argument to establish consistency without assuming sparsity or the existence of any moments of the error matrix, so that fat-tailed continuous random errors such as Cauchy are allowed. The results are illustrated by simulations.

Date: 2019-02, Revised 2019-11
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