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Automated Extraction of Mutual Independence Patterns Using Bayesian Comparison of Partition Models.

Authors
  • Marrelec, Guillaume
  • Giron, Alain
Type
Published Article
Journal
IEEE transactions on pattern analysis and machine intelligence
Publication Date
Jul 01, 2021
Volume
43
Issue
7
Pages
2299–2313
Identifiers
DOI: 10.1109/TPAMI.2020.2968065
PMID: 31985405
Source
Medline
Language
English
License
Unknown

Abstract

Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into the other and used to generate a null distribution for a statistic of interest, usually under the asymptotic assumption of large sample size. As such, these methods have a very restricted scope of application. In this article, we propose to change the investigation of mutual independence from a hypothesis-driven task that can only be applied in very specific cases to a blind and automated search within patterns of mutual independence. To this end, we treat the issue as one of model comparison that we solve in a Bayesian framework. We show the relationship between such an approach and existing methods in the case of multivariate normal distributions as well as cross-classified multinomial distributions. We propose a general Markov chain Monte Carlo (MCMC) algorithm to numerically approximate the posterior distribution on the space of all patterns of mutual independence. The relevance of the method is demonstrated on synthetic data as well as two real datasets, showing the unique insight provided by this approach.

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