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-rankmatrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and aWishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, we develop a variational Bayesian matrix completion method, which embeds the generalized approximate massage passing technique to circumvent cumbersome matrix inverse operations. Simulation results show that our proposedmethod demonstrates superiority over some state-of the-art matrix completion methods.