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May 2020 Reliable clustering of Bernoulli mixture models
Amir Najafi, Seyed Abolfazl Motahari, Hamid R. Rabiee
Bernoulli 26(2): 1535-1559 (May 2020). DOI: 10.3150/19-BEJ1173


A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity analysis in social networks. In this paper, we analyze the clusterability of BMMs from a theoretical perspective, when the number of clusters is unknown. In particular, we stipulate a set of conditions on the sample complexity and dimension of the model in order to guarantee the Probably Approximately Correct (PAC)-clusterability of a dataset. To the best of our knowledge, these findings are the first non-asymptotic bounds on the sample complexity of learning or clustering BMMs.


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Amir Najafi. Seyed Abolfazl Motahari. Hamid R. Rabiee. "Reliable clustering of Bernoulli mixture models." Bernoulli 26 (2) 1535 - 1559, May 2020.


Received: 1 June 2019; Revised: 1 October 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166573
MathSciNet: MR4058377
Digital Object Identifier: 10.3150/19-BEJ1173

Keywords: High-dimensional statistics , mixture model analysis , PAC-learnability , sample complexity

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability


Vol.26 • No. 2 • May 2020
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