Robust matrix completion via Novel M-estimator Functions

TL;DR

This paper introduces a new framework for robust matrix completion using nonconvex M-estimator functions that selectively down-weigh outliers, improving accuracy and efficiency over existing methods.

Contribution

A novel framework for generating nonconvex robust loss functions tailored for matrix completion, with proven convergence and superior performance.

Findings

Outperforms existing methods in recovery accuracy

Achieves faster runtimes

Demonstrates robustness against outliers

Abstract

M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions which only down-weigh outlier-corrupted observations. Our framework is then applied to the Welsch, Cauchy and $\ell_p$-norm functions to produce the corresponding robust loss functions. Targeting on the application of robust matrix completion, efficient algorithms based on these functions are developed and their convergence is analyzed. Finally, extensive numerical results demonstrate that the proposed methods are superior to the competitors in terms of recovery accuracy and runtime.