The Nonparametric Metadata Dependent Relational Model.

We introduce the nonparametric metadata dependent relational (NMDR) model, a Bayesian nonparametric stochastic block model for network data. The NMDR allows the entities associated with each node to have mixed membership in an unbounded collection of latent communities. Learned regression models allow these memberships to depend on, and be predicted from, arbitrary node metadata. We develop efficient MCMC algorithms for learning NMDR models from partially observed node relationships. Retrospective MCMC methods allow our sampler to work directly with the infinite stick-breaking representation of the NMDR, avoiding the need for finite truncations. Our results demonstrate recovery of useful latent communities from real-world social and ecological networks, and the usefulness of metadata in link prediction tasks.