Pitman-Yor Diffusion Trees

摘要

We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restric tion to binary branching structure. The gen erative process is described and shown to re sult in an exchangeable distribution over data points. We prove some theoretical proper ties of the model and then present two infer ence methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally effi cient 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.