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

TL;DR

This paper introduces a hierarchical Bayesian approach for low-rank matrix completion that leverages Gaussian and Wishart priors, employing variational inference and GAMP to improve efficiency and accuracy.

Contribution

The paper proposes a novel hierarchical Gaussian prior model combined with GAMP-embedded variational inference for efficient low-rank matrix completion.

Findings

Outperforms existing matrix completion methods in simulations.

Efficiently circumvents matrix inverse operations using GAMP.

Demonstrates superior accuracy and computational efficiency.

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.