  Identifying latent structure in large data matrices is essential for
exploring biological processes. Here, we consider recovering gene co-expression
networks from gene expression data, where each network encodes relationships
between genes that are locally co-regulated by shared biological mechanisms. To
do this, we develop a Bayesian statistical model for biclustering to infer
subsets of co-regulated genes whose covariation may be observed in only a
subset of the samples. Our biclustering method, BicMix, has desirable
properties, including allowing overcomplete representations of the data,
computational tractability, and jointly modeling unknown confounders and
biological signals. Compared with related biclustering methods, BicMix recovers
latent structure with higher precision across diverse simulation scenarios.
Further, we develop a method to recover gene co-expression networks from the
estimated sparse biclustering matrices. We apply BicMix to breast cancer gene
expression data and recover a gene co-expression network that is differential
across ER+ and ER- samples.
