  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.
