Scalable detection of overlapping communities and role assignments in networks via Bayesian probabilistic generative affiliation modeling

A new generative model of directed networks is developed to explain link formation from a Bayesian probabilistic perspective. Essentially, nodes can be affiliated to multiple (or, even, all) communities as well as roles. Affiliations are dichotomized to account for link direction. The unknown strength of node affiliations to communities and roles is captured through latent nonnegative random variables, that are ruled by Gamma priors for better model interpretability. Overall, such random variables are meant to generalize both mixed-membership and directed affiliation modeling, which allows for a differentiated connectivity structure inside communities. The probability of a link between two nodes is governed by a Poisson distribution, whose rate increases with the number of shared community affiliations as well as the strength of their affiliations to the common communities and respective roles. The properties of the Poisson distribution are especially beneficial on sparse networks for faster posterior inference. The latter is implemented by a coordinateascent variational algorithm enabling affiliation exploration and link prediction. The results of a comparative evaluation carried out on several real-world networks show the overcoming performance of the devised approach in community compactness, link prediction and scalability.