Pitman-Yor Diffusion Trees

David A. Knowles, Zoubin Ghahramani
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:467-475, 2011.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-knowles11a, title = {Pitman-Yor Diffusion Trees}, author = {Knowles, David A. and Ghahramani, Zoubin}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {467--475}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/knowles11a/knowles11a.pdf}, url = {https://proceedings.mlr.press/r9/knowles11a.html}, abstract = {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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Pitman-Yor Diffusion Trees %A David A. Knowles %A Zoubin Ghahramani %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-knowles11a %I PMLR %P 467--475 %U https://proceedings.mlr.press/r9/knowles11a.html %V R9 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Knowles, D.A. & Ghahramani, Z.. (2011). Pitman-Yor Diffusion Trees. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:467-475 Available from https://proceedings.mlr.press/r9/knowles11a.html. Reissued by PMLR on 04 October 2026.

Related Material