Beta Diffusion Trees. Heaukulani, C., <b>Knowles</b>, D. A., & Ghahramani, Z. In *Proceedings of The 31st International Conference on Machine Learning*, pages 1809--1817, 2014. Paper abstract bibtex We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet diffusion tree (Neal, 2003b), which defines a tree structure over partitions (i.e., non-overlapping subsets) of the objects. Unlike in the Dirichlet diffusion tree, multiple copies of a particle may exist and diffuse along multiple branches in the beta diffusion tree, and an object may therefore belong to multiple subsets of particles. We demonstrate how to build a hierarchically-clustered factor analysis model with the beta diffusion tree and how to perform inference over the random tree structures with a Markov chain Monte Carlo algorithm. We conclude with several numerical experiments on missing data problems with data sets of gene expression microarrays, international development statistics, and intranational socioeconomic measurements.

@inproceedings{Heaukulani2014beta,
abstract = {We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet diffusion tree (Neal, 2003b), which defines a tree structure over partitions (i.e., non-overlapping subsets) of the objects. Unlike in the Dirichlet diffusion tree, multiple copies of a particle may exist and diffuse along multiple branches in the beta diffusion tree, and an object may therefore belong to multiple subsets of particles. We demonstrate how to build a hierarchically-clustered factor analysis model with the beta diffusion tree and how to perform inference over the random tree structures with a Markov chain Monte Carlo algorithm. We conclude with several numerical experiments on missing data problems with data sets of gene expression microarrays, international development statistics, and intranational socioeconomic measurements.},
archivePrefix = {arXiv},
arxivId = {1408.3378},
author = {Heaukulani, Creighton and <b>Knowles</b>, David A. and Ghahramani, Zoubin},
booktitle = {Proceedings of The 31st International Conference on Machine Learning},
eprint = {1408.3378},
isbn = {9781634393973},
number = {2011},
pages = {1809--1817},
title = {{Beta Diffusion Trees}},
url = {http://proceedings.mlr.press/v32/heaukulani14.pdf},
keywords = {Machine Learning/Statistics},
year = {2014}
}

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