Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study

摘要

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 [1] and convex relaxation [2], 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.