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

Linxiao Yang, Jun Fang, Huiping Duan, Hongbin Li, Bing Zeng

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

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, 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 proposed method demonstrates superiority over some state-of-the-art matrix completion methods.

Original languageEnglish
Pages (from-to)2804-2817
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume66
Issue number11
DOIs
StatePublished - 1 Jun 2018

Keywords

  • Matrix completion
  • generalized approximate massage passing
  • low-rank Bayesian learning

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