On-line expectation-maximization algorithm for latent data models

We propose a generic on-line (also sometimes called adaptive or recursive) version of the expectation-maximization (EM) algorithm applicable to latent variable models of independent observations. Compared with the algorithm of Titterington, this approach is more directly connected to the usual EM al...

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Vydáno v:	Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 71; číslo 3; s. 593 - 613
Hlavní autoři:	Cappé, Olivier, Moulines, Eric
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.06.2009 Blackwell Publishing Ltd Blackwell Publishing Blackwell Royal Statistical Society Oxford University Press
Edice:	Journal of the Royal Statistical Society Series B
Témata:	Adaptive algorithms Algorithms Approximation Convergence Data Data models Distribution Distribution theory Exact sciences and technology Expectation-maximization General topics Internet Latent data models Linear regression Mathematical analysis Mathematical models Mathematics Matrices Maximum likelihood estimation Measure and integration Mixture of regressions On-line estimation Parametric inference Parametric models Polyak-Ruppert averaging Probabilities Probability and statistics probability distribution Probability theory and stochastic processes Recursion Regression analysis Sciences and techniques of general use Statistical methods Statistical models Statistics Stochastic approximation Stochastic models Studies Conditional distribution Divergence Adaptive algorithm Stochastic approximation Latent data models On-line estimation Linear model Convergence Hypothesis test Statistical test Sequential method Marginal distribution Distribution function Mixed distribution Integration Expectation―maximization Maximization Mixture of Linear regression Adaptive algorithms Latent variable model regressions Independent variable Statistical method Statistical regression Polyak―Ruppert averaging Regression model Maximum likelihood Expectation EM algorithm
ISSN:	1369-7412, 1467-9868
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Popis
Shrnutí:	We propose a generic on-line (also sometimes called adaptive or recursive) version of the expectation-maximization (EM) algorithm applicable to latent variable models of independent observations. Compared with the algorithm of Titterington, this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete-data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e. that of the maximum likelihood estimator. In addition, the approach proposed is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.
Bibliografie:	http://dx.doi.org/10.1111/j.1467-9868.2009.00698.x istex:E2609E9328DE5FE711064DD5372E693A31AF7354 ark:/67375/WNG-LJHDP3BQ-S ArticleID:RSSB698 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 ObjectType-Article-1 ObjectType-Feature-2
ISSN:	1369-7412 1467-9868
DOI:	10.1111/j.1467-9868.2009.00698.x