David Knowles (University of Cambridge)

Diffusion trees as priors

The Dirichlet diffusion tree [Neal, 2001] has attractive theoretical properties and empirical performance on various tasks. We present an extension which removes the restriction to binary trees allowing arbitrary branching structure, the Pitman Yor diffusion tree. We show this process is exchangeable and projective. Both the DDT and PYDT can be constructed as continuum limits of nested CRP models. We demonstrate efficient deterministic and sampling based inference. Finally we discuss some open modelling questions, such as whether to use fragmentation or coalescent processes as priors in hierarchical clustering, and what types of diffusion processes should be preferred.