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2020 Rate optimal Chernoff bound and application to community detection in the stochastic block models
Zhixin Zhou, Ping Li
Electron. J. Statist. 14(1): 1302-1347 (2020). DOI: 10.1214/20-EJS1686

Abstract

The Chernoff coefficient is known to be an upper bound of Bayes error probability in classification problem. In this paper, we will develop a rate optimal Chernoff bound on the Bayes error probability. The new bound is not only an upper bound but also a lower bound of Bayes error probability up to a constant factor. Moreover, we will apply this result to community detection in the stochastic block models. As a clustering problem, the optimal misclassification rate of community detection problem can be characterized by our rate optimal Chernoff bound. This can be formalized by deriving a minimax error rate over certain parameter space of stochastic block models, then achieving such an error rate by a feasible algorithm employing multiple steps of EM type updates.

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Zhixin Zhou. Ping Li. "Rate optimal Chernoff bound and application to community detection in the stochastic block models." Electron. J. Statist. 14 (1) 1302 - 1347, 2020. https://doi.org/10.1214/20-EJS1686

Information

Received: 1 June 2019; Published: 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07200230
MathSciNet: MR4079459
Digital Object Identifier: 10.1214/20-EJS1686

Subjects:
Primary: 62F03
Secondary: 60G05

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Vol.14 • No. 1 • 2020
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