Fast Variational Inference for Joint Mixed Sparse Graphical Models

Abstract

Mixed graphical models are widely implemented to capture interactions among different types of variables. To simultaneously learn the topology of multiple mixed graphical models and encourage common structure, people have developed a variational maximum likelihood inference approach, which takes advantage of the log-determinant relaxation. In this article, we further improve the computational efficiency of this method by exploiting the block diagonal structure of the solution. We present a simple necessary and sufficient condition to identify the connected components in the solution, so as to determine the block diagonal structure. Then, utilizing the idea of “divide-and-conquer”, we are able to adapt the joint structural inference problem for multiple related large sparse networks. We illustrate the merits of the proposed algorithm via experimental comparisons in computational speed.