Tree-Structured Stick Breaking Processes for Hierarchical Data

Details Tree-Structured Stick Breaking Processes for Hierarchical Data Tree-Structured Stick Breaking Processes for Hierarchical Data

2010-06-05

arxiv.org/abs/1006.1062v1

Statistics

Methodology

16 pages, 5 figures, submitted

Scientific paper

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

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