Mixed-Membership Stochastic Block Models for Weighted Networks

We address in this study the problem of modeling weighted networks through generalized stochastic block models. Stochastic block models, and their extensions through mixed-membership versions, are indeed popular methods for network analysis as they can account for the underlying classes/communities structuring real-world networks and can be used for different applications. Our goal is to develop such models to solve the weight prediction problem that consists in predicting weights on links in weighted networks. To do so, we introduce new mixed-membership stochastic block models that can efficiently be learned through a coupling of collapsed and stochastic variational inference. These models, that represent the first weighted mixed-membership stochastic block models to our knowledge, can be deployed on large networks comprising millions of edges. The experiments, conducted on diverse real-world networks, illustrate the good behavior of these new models.