Estimating parameters of a multipartite loglinear graph model via the EM algorithm

Abstract

We will amalgamate the Rash model (for rectangular binary tables) and the newly introduced $\alpha$-$\beta$ models (for random undirected graphs) in the framework of a semiparametric probabilistic graph model. Our purpose is to give a partition of the vertices of an observed graph so that the generated subgraphs and bipartite graphs obey these models, where their strongly connected parameters give multiscale evaluation of the vertices at the same time. In this way, a heterogeneous version of the stochastic block model is built via mixtures of loglinear models and the parameters are estimated with a special EM iteration. In the context of social networks, the clusters can be identified with social groups and the parameters with attitudes of people of one group towards people of the other, which attitudes depend on the cluster memberships. The algorithm is applied to randomly generated and real-word data.