PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Message Passing Algorithms for the Dirichlet Diffusion Tree
David Knowles, Jurgen van Gael and Zoubin Ghahramani
In: ICML 2011(2011).

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.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:8457
Deposited By:David Knowles
Deposited On:19 January 2012