Bayesian methods for low-rank matrix estimation: short survey and theoretical study
This work provides a theoretical foundation for Bayesian methods in low-rank matrix estimation, which is incremental as it extends existing results to a less explored approach.
The paper surveys Bayesian methods for low-rank matrix estimation and proves that, under suitable assumptions, these Bayesian estimators achieve optimality properties comparable to penalization-based approaches.
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.