Pitman-Yor Diffusion Trees

Details Pitman-Yor Diffusion Trees Pitman-Yor Diffusion Trees

2011-06-13

arxiv.org/abs/1106.2494v2

Statistics

Machine Learning

8 pages, to be presented at UAI 2011

Scientific paper

We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which 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 and then present two inference methods: a collapsed MCMC sampler 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.

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