Multi-way Blockmodels for Analyzing Coordinated High-dimensional Responses.

We consider the problem of quantifying temporal coordination between multiple high-dimensional responses. We introduce a family of multi-way stochastic blockmodels suited for this problem, which avoids pre-processing steps such as binning and thresholding commonly adopted for this type of problems, in biology. We develop two inference procedures based on collapsed Gibbs sampling and variational methods. We provide a thorough evaluation of the proposed methods on simulated data, in terms of membership and blockmodel estimation, predictions out-of-sample, and run-time. We also quantify the effects of censoring procedures such as binning and thresholding on the estimation tasks. We use these models to carry out an empirical analysis of the functional mechanisms driving the coordination between gene expression and metabolite concentrations during carbon and nitrogen starvation, in S. cerevisiae.