Optimal Bayesian estimators for latent variable cluster models

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Title: Optimal Bayesian estimators for latent variable cluster models
Authors: Rastelli, RiccardoFriel, Nial
Permanent link: http://hdl.handle.net/10197/10608
Date: 31-Oct-2017
Online since: 2019-05-22T10:23:08Z
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 theoretic 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 a variety of real-data applications for three different clustering models: Gaussian finite mixtures, stochastic block models and latent block models for networks.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Springer
Journal: Statistics and Computing.
Volume: 28
Issue: 6
Start page: 1169
End page: 1186
Copyright (published version): 2017 the Authors
Keywords: Bayesian clusteringCluster analysisGreedy optimisationLatent variable modelsMarkov chain Monte Carlo
DOI: 10.1007/s11222-017-9786-y
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection
Insight Research Collection

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