  This paper describes the hierarchical infinite relational model (HIRM), a new
probabilistic generative model for noisy, sparse, and heterogeneous relational
data. Given a set of relations defined over a collection of domains, the model
first infers multiple non-overlapping clusters of relations using a top-level
Chinese restaurant process. Within each cluster of relations, a Dirichlet
process mixture is then used to partition the domain entities and model the
probability distribution of relation values. The HIRM generalizes the standard
infinite relational model and can be used for a variety of data analysis tasks
including dependence detection, clustering, and density estimation. We present
new algorithms for fully Bayesian posterior inference via Gibbs sampling. We
illustrate the efficacy of the method on a density estimation benchmark of
twenty object-attribute datasets with up to 18 million cells and use it to
discover relational structure in real-world datasets from politics and
genomics.
