Open Access
February 1999 Convergence of a stochastic approximation version of the EM algorithm
Bernard Delyon, Marc Lavielle, Eric Moulines
Ann. Statist. 27(1): 94-128 (February 1999). DOI: 10.1214/aos/1018031103


The expectation-maximization (EM) algorithm is a powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations, however, this method is not applicable because the expectation step cannot be performed in closed form. To deal with these problems, a novel method is introduced, the stochastic approximation EM (SAEM), which replaces the expectation step of the EM algorithm by one iteration of a stochastic approximation procedure. The convergence of the SAEM algorithm is established under conditions that are applicable to many practical situations. Moreover, it is proved that, under mild additional conditions, the attractive stationary points of the SAEM algorithm correspond to the local maxima of the function presented to support our findings.


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Bernard Delyon. Marc Lavielle. Eric Moulines. "Convergence of a stochastic approximation version of the EM algorithm." Ann. Statist. 27 (1) 94 - 128, February 1999.


Published: February 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0932.62094
MathSciNet: MR1701103
Digital Object Identifier: 10.1214/aos/1018031103

Primary: 62F10 , 65U05
Secondary: 60K35 , 62M30

Keywords: EM algorithm , incomplete data , maximum likelihood , missing data , Monte Carlo algorithm , optimization , simulation , Stochastic algorithm

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 1 • February 1999
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