Murphy, Keefe and Viroli, Cinzia and Gormley, Isobel Claire (2020) Infinite Mixtures of Infinite Factor Analysers. Bayesian Analysis, 15 (3). pp. 937-963. ISSN 1931-6690

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Abstract

Factor-analytic Gaussian mixtures are often employed as a model-based approach to clustering high-dimensional data. Typically, the numbers of clusters and latent factors must be fixed in advance of model fitting. The pair which optimises some model selection criterion is then chosen. For computational reasons, having the number of factors differ across clusters is rarely considered. Here the infinite mixture of infinite factor analysers (IMIFA) model is introduced. IMIFA employs a Pitman-Yor process prior to facilitate automatic inference of the number of clusters using the stick-breaking construction and a slice sampler. Automatic inference of the cluster-specific numbers of factors is achieved using multiplicative gamma process shrinkage priors and an adaptive Gibbs sampler. IMIFA is presented as the flagship of a family of factor-analytic mixtures. Applications to benchmark data, metabolomic spectral data, and a handwritten digit example illustrate the IMIFA model’s advantageous features. These include obviating the need for model selection criteria, reducing the computational burden associated with the search of the model space, improving clustering performance by allowing cluster-specific numbers of factors, and uncertainty quantification.

Item Type:	Article
Additional Information:	Cite as: Keefe Murphy. Cinzia Viroli. Isobel Claire Gormley. "Infinite Mixtures of Infinite Factor Analysers." Bayesian Anal. 15 (3) 937 - 963, September 2020. https://doi.org/10.1214/19-BA1179 . Acknowledgments This research was supported by the Science Foundation Ireland funded Insight Centre for Data Analytics in University College Dublin under grant number SFI/12/RC/2289 P2. The authors thank the members of the UCD Working Group in Statistical Learning and Prof. Adrian Raftery’s Working Group in Model-based Clustering and Prof. David Dunson for helpful discussions. The authors also thank Prof. Lorraine Brennan (UCD), for the metabolomic data, and the anonymous reviewers for constructive feedback from which this work greatly benefited
Keywords:	Adaptive Markov chain Monte Carlo; factor analysis; Model-based clustering; multiplicative gamma process; Pitman-Yor process;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	15557
Identification Number:	https://doi.org/10.1214/19-BA1179
Depositing User:	Keefe Murphy
Date Deposited:	22 Feb 2022 17:13
Journal or Publication Title:	Bayesian Analysis
Publisher:	International Society for Bayesian Analysis (ISBA)
Refereed:	Yes
Funders:	Science Foundation Ireland (SFI)
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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