  A hierarchical gamma process infinite edge partition model is proposed to
factorize the binary adjacency matrix of an unweighted undirected relational
network under a Bernoulli-Poisson link. The model describes both homophily and
stochastic equivalence, and is scalable to big sparse networks by focusing its
computation on pairs of linked nodes. It can not only discover overlapping
communities and inter-community interactions, but also predict missing edges. A
simplified version omitting inter-community interactions is also provided and
we reveal its interesting connections to existing models. The number of
communities is automatically inferred in a nonparametric Bayesian manner, and
efficient inference via Gibbs sampling is derived using novel data augmentation
techniques. Experimental results on four real networks demonstrate the models'
scalability and state-of-the-art performance.
