Modeling and Change Detection for Count-Weighted Multilayer Networks

In a typical network with a set of individuals, it is common to have multiple types of interactions between two individuals. In practice, these interactions are usually sparse and correlated, which is not sufficiently accounted for in the literature. This paper proposes a multi-layer weighted stochastic block model (MZIP-SBM) based on a multivariate zero- inflated Poisson (MZIP) distribution to characterize the sparse and correlated multi-layer interactions of individuals. A variational-EM algorithm is developed in order to estimate the parameters in this model. We further propose a monitoring statistic based on the score test of MZIP-SBM model parameters for change detection in multi-layer networks. The proposed model and monitoring scheme are validated using extensive simulation studies and the case study from Enron email network.