Sparse Bayesian Methods for Low-Rank Matrix Estimation

TL;DR

This paper introduces sparse Bayesian learning-based algorithms for low-rank matrix recovery, effectively determining the matrix rank and achieving high accuracy in matrix completion and robust PCA tasks.

Contribution

It presents a novel Bayesian approach that enforces low-rank constraints as sparsity, improving rank estimation and recovery performance over existing methods.

Findings

Effective rank determination in matrix completion.

Superior recovery accuracy compared to state-of-the-art methods.

Connections established with related algorithms.

Abstract

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled method for choosing the unknown target rank is generally not provided. In this paper, we present novel recovery algorithms for estimating low-rank matrices in matrix completion and robust principal component analysis based on sparse Bayesian learning (SBL) principles. Starting from a matrix factorization formulation and enforcing the low-rank constraint in the estimates as a sparsity constraint, we develop an approach that is very effective in determining the correct rank while providing high recovery performance. We provide connections with existing methods in other similar problems and empirical results and comparisons with current state-of-the-art methods that illustrate the effectiveness of this approach.