Pseudo-Bayesian Robust PCA: Algorithms and Analyses

TL;DR

This paper introduces a pseudo-Bayesian robust PCA algorithm that improves outlier detection and subspace recovery, outperforming existing methods with strong theoretical support and practical effectiveness.

Contribution

It proposes a novel pseudo-Bayesian approach that addresses weaknesses in non-convex robust PCA methods, achieving state-of-the-art results with solid analysis.

Findings

Outperforms existing non-convex robust PCA methods

Can surpass convex matrix completion in certain regimes

Provides strong theoretical guarantees for recovery

Abstract

Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into low rank and sparse components, the latter representing unwanted outliers. Although the resulting optimization problem is typically NP-hard, convex relaxations provide a computationally-expedient alternative with theoretical support. However, in practical regimes performance guarantees break down and a variety of non-convex alternatives, including Bayesian-inspired models, have been proposed to boost estimation quality. Unfortunately though, without additional a priori knowledge none of these methods can significantly expand the critical operational range such that exact principal subspace recovery is possible. Into this mix we propose a novel pseudo-Bayesian algorithm that explicitly compensates for design weaknesses in many existing non-convex approaches leading to state-of-the-art performance with a sound analytical foundation. Surprisingly, our algorithm can even outperform convex matrix completion despite the fact that the latter is provided with perfect knowledge of which entries are not corrupted.