Estimation in a binomial stochastic blockmodel for a weighted graph by a variational expectation maximization algorithm

Abstract

Stochastic blockmodels have been widely proposed as a probabilistic random graph model for the analysis of networks data as well as for detecting community structure in these networks. In a number of real-world networks, not all ties among nodes have the same weight. Ties among networks nodes are often associated with weights that differentiate them in terms of their strength, intensity, or capacity. In this paper, we provide an inference method through a variational expectation maximization algorithm to estimate the parameters in binomial stochastic blockmodels for weighted networks. To prove the validity of the method and to highlight its main features, we set some applications of the proposed approach by using some simulated data and then some real data sets. Stochastic blockmodels belong to latent classes models. Classes defines a node's clustering. We compare the clustering found through binomial stochastic blockmodels with the ones found fitting a stochastic blockmodel with Poisson distributed edges. Inferred Poisson and binomial stochastic blockmodels mainly differs. Moreover, in our examples, the statistical error is lower for binomial stochastic blockmodels.

Weighted stochastic block model

“…This assumption is unrealistic for many applications whereby a certain proportion of the real-valued edges is 0. Haj et al (2020) presents a binomial SBM for weighted graphs and proposes a variational expectation maximization algorithm for parameter estimation.…”