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Acceleration of the EM Algorithm by using Quasi‐Newton Methods

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  • Mortaza Jamshidian
  • Robert I. Jennrich

Abstract

The EM algorithm is a popular method for maximum likelihood estimation. Its simplicity in many applications and desirable convergence properties make it very attractive. Its sometimes slow convergence, however, has prompted researchers to propose methods to accelerate it. We review these methods, classifying them into three groups: pure, hybrid and EM‐type accelerators. We propose a new pure and a new hybrid accelerator both based on quasi‐Newton methods and numerically compare these and two other quasi‐Newton accelerators. For this we use examples in each of three areas: Poisson mixtures, the estimation of covariance from incomplete data and multivariate normal mixtures. In these comparisons, the new hybrid accelerator was fastest on most of the examples and often dramatically so. In some cases it accelerated the EM algorithm by factors of over 100. The new pure accelerator is very simple to implement and competed well with the other accelerators. It accelerated the EM algorithm in some cases by factors of over 50. To obtain standard errors, we propose to approximate the inverse of the observed information matrix by using auxiliary output from the new hybrid accelerator. A numerical evaluation of these approximations indicates that they may be useful at least for exploratory purposes.

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  • Mortaza Jamshidian & Robert I. Jennrich, 1997. "Acceleration of the EM Algorithm by using Quasi‐Newton Methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 569-587.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:3:p:569-587
    DOI: 10.1111/1467-9868.00083
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    Cited by:

    1. Fung, Tsz Chai, 2022. "Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 180-198.
    2. Zhou, Lin & Tang, Yayong, 2021. "Linearly preconditioned nonlinear conjugate gradient acceleration of the PX-EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    3. Iain L. MacDonald, 2021. "Is EM really necessary here? Examples where it seems simpler not to use EM," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 629-647, December.
    4. Kaarina Matilainen & Esa A Mäntysaari & Martin H Lidauer & Ismo Strandén & Robin Thompson, 2013. "Employing a Monte Carlo Algorithm in Newton-Type Methods for Restricted Maximum Likelihood Estimation of Genetic Parameters," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-7, December.
    5. Jurgen A. Doornik, 2018. "Accelerated Estimation of Switching Algorithms: The Cointegrated VAR Model and Other Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 283-300, June.
    6. Rasool Roozegar & G. G. Hamedani & Leila Amiri & Fatemeh Esfandiyari, 2020. "A New Family of Lifetime Distributions: Theory, Application and Characterizations," Annals of Data Science, Springer, vol. 7(1), pages 109-138, March.
    7. Saâdaoui, Foued, 2023. "Randomized extrapolation for accelerating EM-type fixed-point algorithms," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    8. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.

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