Open AccessProceedings Article
Message passing algorithms for dirichlet diffusion trees
David A. Knowles,Jurgen Van Gael,Zoubin Ghahramani +2 more
- 28 Jun 2011
- pp 721-728
TL;DR: This work provides the first deterministic approximate inference methods for DDT models and shows excellent performance compared to the MCMC alternative on a density estimation problem, and significantly outperforms kernel density estimators.
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Abstract: We demonstrate efficient approximate inference for the Dirichlet Diffusion Tree (Neal, 2003), a Bayesian nonparametric prior over tree structures. Although DDTs provide a powerful and elegant approach for modeling hierarchies they haven't seen much use to date. One problem is the computational cost of MCMC inference. We provide the first deterministic approximate inference methods for DDT models and show excellent performance compared to the MCMC alternative. We present message passing algorithms to approximate the Bayesian model evidence for a specific tree. This is used to drive sequential tree building and greedy search to find optimal tree structures, corresponding to hierarchical clusterings of the data. We demonstrate appropriate observation models for continuous and binary data. The empirical performance of our method is very close to the computationally expensive MCMC alternative on a density estimation problem, and significantly outperforms kernel density estimators.
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Citations
Pitman Yor Diffusion Trees for Bayesian Hierarchical Clustering
TL;DR: The Pitman Yor Diffusion Tree (PYDT), a Bayesian non-parametric prior over tree structures which generalises the Dirichlet Diffusion tree and removes the restriction to binary branching structure is introduced.
26
•Posted Content
Pitman-Yor Diffusion Trees
TL;DR: The Pitman Yor Diffusion Tree (PYDT) is introduced, a generalization of the Dirichlet Diffusion tree which removes the restriction to binary branching structure and two inference methods are presented: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm.
21
•Proceedings Article
Pitman-Yor Diffusion Trees
David A. Knowles,Zoubin Ghahramani +1 more
- 14 Jul 2011
TL;DR: The Pitman Yor Diffusion Tree (PYDT) as discussed by the authors is a generalization of the Dirichlet diffusion tree for hierarchical clustering, which removes the restriction to binary branching structure.
Random Infinite Tree and Dependent Poisson Diffusion Process for Nonparametric Bayesian Modeling in Multiple Object Tracking
Bahman Moraffah,Antonia Papandreou-Suppappola +1 more
- 12 May 2019
TL;DR: This work proposes a new method to track a dynamically varying number of objects using information from previously tracked ones based on nonparametric Bayesian modeling using diffusion processes and random trees.
15
•Proceedings Article
The Time-Marginalized Coalescent Prior for Hierarchical Clustering
Levi Boyles,Max Welling +1 more
- 03 Dec 2012
TL;DR: A new prior for use in Nonparametric Bayesian Hierarchical Clustering is introduced, constructed by marginalizing out the time information of Kingman's coalescent, providing a prior over tree structures which is called the Time-Marginalized Coalescent (TMC).
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