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

A latent factor model with a mixture of sparse and dense factors to model gene expression data with confounding effects