Poisson degree corrected dynamic stochastic block model

Abstract

Stochastic Block Model (SBM) provides a statistical tool for modeling and clustering network data. In this paper, we propose an extension of this model for discrete-time dynamic networks that takes into account the variability in node degrees, allowing us to model a broader class of networks. We develop a probabilistic model that generates temporal graphs with a dynamic cluster structure and time-dependent degree corrections for each node. Thanks to these degree corrections, the nodes can have variable in- and out-degrees, allowing us to model complex cluster structures as well as interactions that decrease or increase over time. We compare the proposed model to a model without degree correction and highlight its advantages in the case of inhomogenous degree distributions in the clusters and in the recovery of unstable cluster dynamics. We propose an inference procedure based on Variational Expectation-Maximization (VEM) that also provides the means to estimate the time-dependent degree corrections. Extensive experiments on simulated and real datasets confirm the benefits of our approach and show the effectiveness of the proposed algorithm.