Parallel Markov Chain Monte Carlo for Pitman-Yor Mixture Models

The Pitman-Yor process provides an elegant way to cluster data that exhibit power law behavior, where the number of clusters is unknown or un-bounded. Unfortunately, inference in PitmanYor process-based models is typically slow and does not scale well with dataset size. In this paper we present new auxiliary-variable representations for the Pitman-Yor process and a special case of the hierarchical Pitman-Yor process that allows us to develop parallel inference algorithms that distribute inference both on the data space and the model space. We show that our method scales well with increasing data while avoiding any degradation in estimate quality.