Relevance Singular Vector Machine for low-rank matrix sensing

TL;DR

This paper introduces the Relevance Singular Vector Machine (RSVM), a Bayesian approach for low-rank matrix sensing that promotes low rank via priors on singular vectors, with efficient algorithms for matrix completion and reconstruction.

Contribution

The paper presents a novel Bayesian inference method, RSVM, with efficient algorithms and priors on singular vectors for low-rank matrix sensing tasks.

Findings

RSVM effectively promotes low-rank solutions.

The algorithms perform well in matrix completion and reconstruction.

Numerical studies demonstrate the method's efficiency.

Abstract

In this paper we develop a new Bayesian inference method for low rank matrix reconstruction. We call the new method the Relevance Singular Vector Machine (RSVM) where appropriate priors are defined on the singular vectors of the underlying matrix to promote low rank. To accelerate computations, a numerically efficient approximation is developed. The proposed algorithms are applied to matrix completion and matrix reconstruction problems and their performance is studied numerically.