Open Access
2020 Statistical convergence of the EM algorithm on Gaussian mixture models
Ruofei Zhao, Yuanzhi Li, Yuekai Sun
Electron. J. Statist. 14(1): 632-660 (2020). DOI: 10.1214/19-EJS1660


We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated by at least $\Omega (\sqrt{\min \{M,d\}})$, where $M$ is the number of components and $d$ is the dimension, the EM algorithm converges locally to the global optimum of the log-likelihood. Further, we show that the convergence rate is linear and characterize the size of the basin of attraction to the global optimum.


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Ruofei Zhao. Yuanzhi Li. Yuekai Sun. "Statistical convergence of the EM algorithm on Gaussian mixture models." Electron. J. Statist. 14 (1) 632 - 660, 2020.


Received: 1 October 2018; Published: 2020
First available in Project Euclid: 28 January 2020

zbMATH: 07163269
MathSciNet: MR4056269
Digital Object Identifier: 10.1214/19-EJS1660

Primary: 62F10
Secondary: 65K05

Keywords: EM algorithm , Gaussian mixture models

Vol.14 • No. 1 • 2020
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