Variational algorithms for biclustering models

Biclustering is an important tool in exploratory statistical analysis which can be used to detect latent row and column groups of different response patterns. However, few studies include covariate data directly into their biclustering models to explain these variations. A novel biclustering framework that considers both stochastic block structures and covariate effects is proposed to address this modeling problem. Fast approximation estimation algorithms are also developed to deal with a large number of latent variables and covariate coefficients. These algorithms are derived from the variational generalized expectation-maximization (EM) framework where the goal is to increase, rather than maximize, the likelihood lower bound in both E and M steps. The utility of the proposed biclustering framework is demonstrated through two block modeling applications in model-based collaborative filtering and microarray analysis.