Learning Latent Block Structure in Weighted Networks

Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity pat-terns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network’s large-scale structure, which can facilitate its scientific interpre-tation and the prediction of unknown or future interactions. Popular approaches, including the stochastic block model, assume edges are unweighted, which limits their utility by discarding po-tentially useful information. We introduce the weighted stochastic block model (WSBM), which generalizes the stochastic block model to networks with edge weights drawn from any exponen-tial family distribution. This model learns from both the presence and weight of edges, allowing it to discover structure that would otherwise be hidden when weights are discarded or thresh-olded. We describe a Bayesian variational algorithm for efficiently approximating this model’s posterior distribution over latent block structures. We then evaluate the WSBM’s performance on both edge-existence and edge-weight prediction tasks for a set of real-world weighted net-works. In all cases, the WSBM performs as well or better than the best alternatives on these tasks. community detection, weighted relational data, block models, exponential family, variational Bayes.