  We develop the distance dependent Chinese restaurant process (CRP), a
flexible class of distributions over partitions that allows for
non-exchangeability. This class can be used to model many kinds of dependencies
between data in infinite clustering models, including dependencies across time
or space. We examine the properties of the distance dependent CRP, discuss its
connections to Bayesian nonparametric mixture models, and derive a Gibbs
sampler for both observed and mixture settings. We study its performance with
three text corpora. We show that relaxing the assumption of exchangeability
with distance dependent CRPs can provide a better fit to sequential data. We
also show its alternative formulation of the traditional CRP leads to a
faster-mixing Gibbs sampling algorithm than the one based on the original
formulation.
