  One important problem in genome science is to determine sets of co-regulated
genes based on measurements of gene expression levels across samples, where the
quantification of expression levels includes substantial technical and
biological noise. To address this problem, we developed a Bayesian sparse
latent factor model that uses a three parameter beta prior to flexibly model
shrinkage in the loading matrix. By applying three layers of shrinkage to the
loading matrix (global, factor-specific, and element-wise), this model has
non-parametric properties in that it estimates the appropriate number of
factors from the data. We added a two-component mixture to model each factor
loading as being generated from either a sparse or a dense mixture component;
this allows dense factors that capture confounding noise, and sparse factors
that capture local gene interactions. We developed two statistics to quantify
the stability of the recovered matrices for both sparse and dense matrices. We
tested our model on simulated data and found that we successfully recovered the
true latent structure as compared to related models. We applied our model to a
large gene expression study and found that we recovered known covariates and
small groups of co-regulated genes. We validated these gene subsets by testing
for associations between genotype data and these latent factors, and we found a
substantial number of biologically important genetic regulators for the
recovered gene subsets.
