  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.
