Title: Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models,
Abstract: 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 low-rank solution. Based on the proposed hierarchical
prior model, a variational Bayesian method is developed for matrix completion,
where the generalized approximate massage passing (GAMP) technique is embedded
into the variational Bayesian inference in order to circumvent cumbersome
matrix inverse operations. Simulation results show that our proposed method
demonstrates superiority over existing state-of-the-art matrix completion
methods.