TO APPEAR IN: IEEE TPAMI SI ON BAYESIAN NONPARAMETRICS 1 Pitman Yor Diffusion Trees for

Abstract—In this paper we introduce the Pitman Yor Diffusion Tree (PYDT), a Bayesian non-parametric prior over tree structures which generalises the Dirichlet Diffusion Tree [Neal, 2001] and removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model including showing its construction as the continuum limit of a nested Chinese restaurant process model. We then present two alternative MCMC samplers which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary. Index Terms—Machine learning, unsupervised learning, clustering methods, phylogeny, density estimation, robust algorithm F