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A new class of stochastic EM algorithms. Escaping local maxima and handling intractable sampling

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  • Allassonnière, Stéphanie
  • Chevallier, Juliette

Abstract

The expectation–maximization (EM) algorithm is a powerful computational technique for maximum likelihood estimation in incomplete data models. When the expectation step cannot be performed in closed form, a stochastic approximation of EM (SAEM) can be used. The convergence of the SAEM toward critical points of the observed likelihood has been proved and its numerical efficiency has been demonstrated. However, sampling from the posterior distribution may be intractable or have a high computational cost. Moreover, despite appealing features, the limit position of this algorithm can strongly depend on its starting one. Sampling from an approximation of the distribution in the expectation phase of the SAEM allows coping with these two issues. This new procedure is referred to as approximated-SAEM and is proved to converge toward critical points of the observed likelihood. Experiments on synthetic and real data highlight the performance of this algorithm in comparison to the SAEM and the EM when feasible.

Suggested Citation

  • Allassonnière, Stéphanie & Chevallier, Juliette, 2021. "A new class of stochastic EM algorithms. Escaping local maxima and handling intractable sampling," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:csdana:v:159:y:2021:i:c:s0167947320302504
    DOI: 10.1016/j.csda.2020.107159
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    References listed on IDEAS

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    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Ravi Varadhan & Christophe Roland, 2008. "Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 335-353, June.
    3. Xiao‐Li Meng & David Van Dyk, 1997. "The EM Algorithm—an Old Folk‐song Sung to a Fast New Tune," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 511-567.
    4. Jank, Wolfgang, 2005. "Quasi-Monte Carlo sampling to improve the efficiency of Monte Carlo EM," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 685-701, April.
    5. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    6. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    7. Glenn Milligan, 1980. "An examination of the effect of six types of error perturbation on fifteen clustering algorithms," Psychometrika, Springer;The Psychometric Society, vol. 45(3), pages 325-342, September.
    8. Umberto Picchini & Adeline Samson, 2018. "Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models," Computational Statistics, Springer, vol. 33(1), pages 179-212, March.
    9. repec:dau:papers:123456789/5724 is not listed on IDEAS
    10. Samson, Adeline & Lavielle, Marc & Mentre, France, 2006. "Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1562-1574, December.
    11. Kuhn, E. & Lavielle, M., 2005. "Maximum likelihood estimation in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1020-1038, June.
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    2. Gámiz, María Luz & Mammen, Enno & Martínez-Miranda, María Dolores & Nielsen, Jens Perch, 2022. "Missing link survival analysis with applications to available pandemic data," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).

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