Convergence of a stochastic approximation version of the EM algorithm

1999/03/01 by Bernard Delyon, Marc Lavielle, Eric Moulines +1 · 779 citations
Economics, Econometrics and Finance · Mathematics · #A priori and a posteriori #Algorithm #Applied mathematics #Approximation algorithm #Computer science #Convergence (economics) #Expectation–maximization algorithm #Markov Chains and Monte Carlo Methods #Mathematical optimization #Mathematics #Maxima #Maxima and minima #Maximization #Maximum a posteriori estimation #Maximum likelihood #Statistical Methods and Inference #Statistics #Stochastic approximation #Stochastic processes and financial applications

paper · pdf · doi:10.1214/aos/1018031103

published in The Annals of Statistics 27(1) (Institute of Mathematical Statistics)

openalex publication_date 1999/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

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.

Citations

• On the Convergence Properties of the EM Algorithm

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