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June 2011 Hierarchical Bayesian nonparametric mixture models for clustering with variable relevance determination
Christopher Yau, Chris Holmes
Bayesian Anal. 6(2): 329-351 (June 2011). DOI: 10.1214/11-BA612

Abstract

We propose a hierarchical Bayesian nonparametric mixture model for clustering when some of the covariates are assumed to be of varying relevance to the clustering problem. This can be thought of as an issue in variable selection for unsupervised learning. We demonstrate that by defining a hierarchical population based nonparametric prior on the cluster locations scaled by the inverse covariance matrices of the likelihood we arrive at a `sparsity prior' representation which admits a conditionally conjugate prior. This allows us to perform full Gibbs sampling to obtain posterior distributions over parameters of interest including an explicit measure of each covariate's relevance and a distribution over the number of potential clusters present in the data. This also allows for individual cluster specific variable selection. We demonstrate improved inference on a number of canonical problems.

Citation

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Christopher Yau. Chris Holmes. "Hierarchical Bayesian nonparametric mixture models for clustering with variable relevance determination." Bayesian Anal. 6 (2) 329 - 351, June 2011. https://doi.org/10.1214/11-BA612

Information

Published: June 2011
First available in Project Euclid: 13 June 2012

zbMATH: 1330.62265
MathSciNet: MR2806247
Digital Object Identifier: 10.1214/11-BA612

Subjects:
Primary: 62H30
Secondary: 60G57, 62B10, 62F15, 62G99, 62H99, 62P10

Rights: Copyright © 2011 International Society for Bayesian Analysis

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Vol.6 • No. 2 • June 2011
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