CUED Publications database

Beta diffusion trees

Heaukulani, C and Knowles, DA and Ghahramani, Z (2014) Beta diffusion trees. In: UNSPECIFIED pp. 3821-3829..

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Abstract

Copyright 2014 by the author(s). 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. The generative process for the tree is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet and Pitman-Yor diffusion trees (Neal, 2003b; Knowles & Ghahramani, 2011), both of which define tree structures over clusters of the particles. With the beta diffusion tree, however, multiple copies of a particle may exist and diffuse to multiple locations in the continuous space, resulting in (a random number of) possibly overlapping clusters of the objects. 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 arrays, international development statistics, and intranational socioeconomic measurements.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Subjects: UNSPECIFIED
Divisions: Div F > Computational and Biological Learning
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:45
Last Modified: 03 Aug 2017 03:15
DOI: