Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models

The problem of low-rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a lowrank solution. Based on the proposed hierarchical prior model, we develop a variational Bayesian matrix completion method which embeds the generalized approximate massage passing (GAMP) technique to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over some state-of-the-art matrix completion methods.