Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing.

Journal Article (Journal Article)

We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate "artificial" posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data.

Full Text

Duke Authors

Cited Authors

  • Yoshida, R; West, M

Published Date

  • May 2010

Published In

Volume / Issue

  • 11 /

Start / End Page

  • 1771 - 1798

PubMed ID

  • 20890391

Pubmed Central ID

  • PMC2947451

Electronic International Standard Serial Number (EISSN)

  • 1533-7928

International Standard Serial Number (ISSN)

  • 1532-4435


  • eng