Multi-way blockmodels for analyzing coordinated high-dimensional responses

Abstract

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 preprocessing steps such as binning and thresholding com- monly adopted for this type of data, in biology. We develop two in- ference 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 estima- tion, 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 be- tween gene expression and metabolite concentrations during carbon and nitrogen starvation, in S. cerevisiae.