Log-linear stochastic block modeling and monitoring of directed sparse weighted network systems

Networks have been widely employed to reflect the relationships of entities in complex systems. In a weighted network, each node corresponds to one entity while the edge weight between two nodes can represent the number of interactions between two associated entities. More and more schemes have been established to monitor the networks, which help identify the possible changes or anomalies in corresponding systems. However, limited works can comprehensively reflect the community structure, node heterogeneity, interaction sparsity and direction of weighted networks in the literature. This article proposes a log-linear stochastic block model with latent features of nodes based on the mixture of Bernoulli distribution and Poisson distribution to characterize the sparse directional interaction counts within network systems. Explicit matrices and vectors are designed to incorporate community structure and enable straightforward maximum likelihood estimation of parameters. We further construct a monitoring statistic based on the generalized likelihood ratio test for change detection of sparse weighted networks. Comparative studies based on simulations and real data are conducted to validate the high efficiency of proposed model and monitoring scheme.