Optimal Bayesian estimators for latent variable cluster models

Rastelli, Riccardo and Friel, Nial (2018) Optimal Bayesian estimators for latent variable cluster models. Statistics and Computing, 28 (6). pp. 1169-1186. ISSN 0960-3174

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Abstract

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretical approach to define an optimality criterion for clusterings and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on both artificial and real datasets for three different clustering models: Gaussian mixtures, stochastic block models and latent block models for networks.

Item Type: Article
Additional Information: Open access funding provided by Vienna University of Economics and Business (WU). The authors' research was supported by a Science Foundation Ireland Grant: 12/IP/1424. The Insight Centre for Data Analytics is supported by Science Foundation Ireland under Grant No. SFI/12/RC/2289. Riccardo Rastelli's research was also funded through the Vienna Science and Technology Fund (WWTF) Project MA14-031.
Keywords: Bayesian clustering, Cluster analysis, Greedy optimisation, Latent variable models, Markov chain Monte Carlo
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Version of the Document: Published
Depositing User: ePub Administrator
Date Deposited: 02 Nov 2017 09:49
Last Modified: 20 Feb 2019 22:26
Related URLs:
URI: https://epub.wu.ac.at/id/eprint/5837

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