Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing.
Abstract
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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/4635Collections
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Mike West
Arts and Sciences Distinguished Professor of Statistics and Decision Sciences
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