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June 2018 Bayesian Cluster Analysis: Point Estimation and Credible Balls (with Discussion)
Sara Wade, Zoubin Ghahramani
Bayesian Anal. 13(2): 559-626 (June 2018). DOI: 10.1214/17-BA1073

Abstract

Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to popular algorithms such as agglomerative hierarchical clustering or k-means which return a single clustering solution, Bayesian nonparametric models provide a posterior over the entire space of partitions, allowing one to assess statistical properties, such as uncertainty on the number of clusters. However, an important problem is how to summarize the posterior; the huge dimension of partition space and difficulties in visualizing it add to this problem. In a Bayesian analysis, the posterior of a real-valued parameter of interest is often summarized by reporting a point estimate such as the posterior mean along with 95% credible intervals to characterize uncertainty. In this paper, we extend these ideas to develop appropriate point estimates and credible sets to summarize the posterior of the clustering structure based on decision and information theoretic techniques.

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Sara Wade. Zoubin Ghahramani. "Bayesian Cluster Analysis: Point Estimation and Credible Balls (with Discussion)." Bayesian Anal. 13 (2) 559 - 626, June 2018. https://doi.org/10.1214/17-BA1073

Information

Published: June 2018
First available in Project Euclid: 19 October 2017

zbMATH: 06989960
MathSciNet: MR3807860
Digital Object Identifier: 10.1214/17-BA1073

Keywords: Binder’s loss , mixture model , random partition , variation of information

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Vol.13 • No. 2 • June 2018
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