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Improving the vector $$\varepsilon $$ ε acceleration for the EM algorithm using a re-starting procedure

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  • Masahiro Kuroda
  • Zhi Geng
  • Michio Sakakihara

Abstract

The expectation–maximization (EM) algorithm is a popular algorithm for finding maximum likelihood estimates from incomplete data. However, the EM algorithm converges slowly when the proportion of missing data is large. Although many acceleration algorithms have been proposed, they require complex calculations. Kuroda and Sakakihara (Comput Stat Data Anal 51:1549–1561, 2006 ) developed the $$\varepsilon $$ ε -accelerated EM algorithm which only uses the sequence of estimates obtained by the EM algorithm to get an accelerated sequence for the EM sequence but does not change the original EM sequence. We find that the accelerated sequence often has larger values of the likelihood than the current estimate obtained by the EM algorithm. Thus, in this paper, we try to re-start the EM iterations using the accelerated sequence and then generate a new EM sequence that increases its speed of convergence. This algorithm has another advantage of simple implementation since it only uses the EM iterations and re-starts the iterations by an estimate with a larger likelihood. The re-starting algorithm called the $$\varepsilon $$ ε R-accelerated EM algorithm can further improve the EM algorithm and the $$\varepsilon $$ ε -accelerated EM algorithm in the sense of that it can reduces the number of iterations and computation time. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Masahiro Kuroda & Zhi Geng & Michio Sakakihara, 2015. "Improving the vector $$\varepsilon $$ ε acceleration for the EM algorithm using a re-starting procedure," Computational Statistics, Springer, vol. 30(4), pages 1051-1077, December.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:4:p:1051-1077
    DOI: 10.1007/s00180-015-0565-y
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    References listed on IDEAS

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    1. Mingfeng Wang & Masahiro Kuroda & Michio Sakakihara & Zhi Geng, 2008. "Acceleration of the EM algorithm using the vector epsilon algorithm," Computational Statistics, Springer, vol. 23(3), pages 469-486, July.
    2. Lee, Gyemin & Scott, Clayton, 2012. "EM algorithms for multivariate Gaussian mixture models with truncated and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2816-2829.
    3. Kuroda, Masahiro & Sakakihara, Michio, 2006. "Accelerating the convergence of the EM algorithm using the vector [epsilon] algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1549-1561, December.
    4. 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.
    5. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
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