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Linearly preconditioned nonlinear conjugate gradient acceleration of the PX-EM algorithm

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  • Zhou, Lin
  • Tang, Yayong

Abstract

The EM algorithm is a widely applicable algorithm for modal estimation but often criticized for its slow convergence. A new hybrid accelerator named APX-EM is proposed for speeding up the convergence of EM algorithm, which is based on both Linearly Preconditioned Nonlinear Conjugate Gradient (PNCG) and PX-EM algorithm. The intuitive idea is that, each step of the PX-EM algorithm can be viewed approximately as a generalized gradient just like the EM algorithm, then the linearly PNCG method can be used to accelerate the EM algorithm. Essentially, this method is an adjustment of the AEM algorithm, and it usually achieves a faster convergence rate than the AEM algorithm by sacrificing a little simplicity. The convergence of the APX-EM algorithm, includes a global convergence result for this method under suitable conditions, is discussed. This method is illustrated for factor analysis and a random-effects model.

Suggested Citation

  • Zhou, Lin & Tang, Yayong, 2021. "Linearly preconditioned nonlinear conjugate gradient acceleration of the PX-EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:csdana:v:155:y:2021:i:c:s016794732030147x
    DOI: 10.1016/j.csda.2020.107056
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    References listed on IDEAS

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    1. 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.
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    4. 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.
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