Bayesian methods for low-rank matrix estimation: short survey and theoretical study

Abstract

The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the different type of priors considered on matrices to favour low-rank. We also prove that the obtained Bayesian estimators, under suitable assumptions, enjoys the same optimality properties as the ones based on penalization.

Corrected version of a paper published in the proceedings of ALT 2013

References in corpus (3)

• Matrix Completion With Noise
• Pac-bayesian bounds for sparse regression estimation with exponential weights
• Rank penalized estimation of a quantum system

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