Probabilistic analysis of communities and inner roles in networks: Bayesian generative models and approximate inference

Two fundamental tasks in network analysis are community discovery and role assignment. Hitherto, these have been conducted separately. We argue that their integration provides a deeper understanding of connectivity patterns and present unsupervised learning approaches to the exploratory analysis of communities and inner roles of nodes across their interactions in directed networks. In particular, we propose two Bayesian probabilistic models of network interactions that seamlessly integrate community discovery and role assignment. One is the model of a generative process, in which pairs of nodes in a network are associated with communities and roles in the context of their communities; before that an interaction is possibly established between them. According to the generative semantics of such a model, nodes are represented as probability distributions over communities, while communities are viewed as probability distributions over roles. The other model specifies a generative process based on link partitioning, that associates pairs of nodes with respective roles and then assigns their possible interaction to one link community. This is accomplished by representing nodes as probability distributions over roles and, additionally, by explicitly modeling how roles interact with each other. The foresaid distributions are unknown parameters of the proposed models that are estimated from the observed network interactions through suitable Markov Chain Monte Carlo algorithms for approximated posterior inference and parameter estimation. One model overcomes state-of-the-art competitors in link-prediction over real-world networks. The other exhibits a competitive predictive power. Both models overcome an established probabilistic competitor at identifying relatively recognizable structure in synthetic networks.