An Alternative Prior Process for Nonparametric Bayesian Clustering
Prior distributions play a crucial role in Bayesian approaches to clustering. Two commonly-used prior distributions are the Dirichlet and Pitman-Yor processes. In this paper, we investigate the predictive probabilities that underlie these processes, and the implicit \rich-get-richer" characteristic of the resulting partitions. We explore an alternative prior for nonparametric Bayesian clustering, the uniform process, for applications where the \rich-get-richer" property is undesirable. We also explore the cost of this new process: partitions are no longer exchangeable with respect to the ordering of variables. We present new asymptotic and simulationbased results for the clustering characteristics of the uniform process and compare these with known results for the Dirichlet and Pitman-Yor processes. Finally, we compare performance on a real-world document clustering task, demonstrating the practical advantage of the uniform process despite its lack of exchangeability over orderings.