Bayesian Learning for Low-Rank matrix reconstruction

TL;DR

This paper introduces Bayesian latent variable models for low-rank matrix completion from linear measurements, capable of reconstructing matrices without prior knowledge of rank or noise, using evidence approximation and EM algorithms.

Contribution

It presents novel Bayesian methods that effectively reconstruct low-rank matrices in under-determined systems without prior rank or noise information.

Findings

Accurate low-rank matrix reconstruction demonstrated in simulations

Relations established between models and low-rank promoting penalties

Methods outperform existing approaches in various scenarios

Abstract

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the latent variable models and several low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use evidence approximation and expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations.