Open Access
August 2020 Identifiability of nonparametric mixture models and Bayes optimal clustering
Bryon Aragam, Chen Dan, Eric P. Xing, Pradeep Ravikumar
Ann. Statist. 48(4): 2277-2302 (August 2020). DOI: 10.1214/19-AOS1887


Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable by introducing a novel framework involving clustering overfitted parametric (i.e., misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature and are flexible enough to include, for example, mixtures of infinite Gaussian mixtures. In contrast to the recent literature, we allow for general nonparametric mixture components and instead impose regularity assumptions on the underlying mixing measure. As our primary application we apply these results to partition-based clustering, generalizing the notion of a Bayes optimal partition from classical parametric model-based clustering to nonparametric settings. Furthermore, this framework is constructive, so that it yields a practical algorithm for learning identified mixtures, which is illustrated through several examples on real data. The key conceptual device in the analysis is the convex, metric geometry of probability measures on metric spaces and its connection to the Wasserstein convergence of mixing measures. The result is a flexible framework for nonparametric clustering with formal consistency guarantees.


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Bryon Aragam. Chen Dan. Eric P. Xing. Pradeep Ravikumar. "Identifiability of nonparametric mixture models and Bayes optimal clustering." Ann. Statist. 48 (4) 2277 - 2302, August 2020.


Received: 1 November 2018; Revised: 1 July 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134795
Digital Object Identifier: 10.1214/19-AOS1887

Primary: 62G05 , 62H30
Secondary: 62H12

Keywords: Bayes optimal partition , clustering , Identifiability , Mixture models , nonparametric statistics

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 4 • August 2020
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