Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models
This provides an improved method for matrix completion problems, which is incremental but shows competitive performance.
The authors tackled the problem of low-rank matrix completion by proposing a hierarchical Gaussian prior model that encourages low-rank solutions, and developed a variational Bayesian method with embedded GAMP technique to avoid matrix inversions. Their simulation results show superiority over existing state-of-the-art methods.
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.