Spike-and-slab Lasso biclustering

Biclustering methods simultaneously group samples and their associated features. In this way, biclustering methods differ from traditional clustering methods, which utilize the entire set of features to distinguish groups of samples. Motivating applications for biclustering include genomics data, where the goal is to cluster patients or samples by their gene expression profiles; and recommender systems, which seek to group customers based on their product preferences. Biclusters of interest often manifest as rank-1 submatrices of the data matrix. This submatrix detection problem can be viewed as a factor analysis problem in which both the factors and loadings are sparse. In this paper, we propose a new biclustering method called Spike-and-Slab Lasso Biclustering (SSLB) which utilizes the Spike-and-Slab Lasso of Ročková and George (2018) to find such a sparse factorization of the data matrix. SSLB also incorporates an Indian Buffet Process prior to automatically choose the number of biclusters. Many biclustering methods make assumptions about the size of the latent biclusters; either assuming that the biclusters are all of the same size, or that the biclusters are very large or very small. In contrast, SSLB can adapt to find biclusters which have a continuum of sizes. SSLB is implemented via a fast EM algorithm with a variational step. In a variety of simulation settings, SSLB outperforms other biclustering methods. We apply SSLB to both a microarray dataset and a single-cell RNA-sequencing dataset and highlight that SSLB can recover biologically meaningful structures in the data. The SSLB software is available as an R/C++ package at https://github.com/gemoran/SSLB.