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Randomized extrapolation for accelerating EM-type fixed-point algorithms

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  • Saâdaoui, Foued

Abstract

Several extrapolation strategies have been proposed in the literature to accelerate the EM algorithm, with varying degrees of success. One advantage of extrapolation methods is their ease of implementation, as they only require working with the EM iterations and do not need auxiliary quantities, such as gradient and Hessian. In this paper, we introduce a new family of iterative schemes based on vector extrapolation methods. We also construct and numerically test a randomly relaxed version of the scheme. Our results demonstrate that these new strategies can significantly and stably accelerate the convergence of the EM algorithm compared to existing methods. Moreover, these strategies are highly versatile as they can accelerate any linearly convergent fixed point iteration, including EM-type algorithms. Finally, we provide statistical modeling experiments at the end of the paper to demonstrate the applicability and interest of these convergence acceleration schemes, whether applied to the EM algorithm or one of its variants.

Suggested Citation

  • Saâdaoui, Foued, 2023. "Randomized extrapolation for accelerating EM-type fixed-point algorithms," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:jmvana:v:196:y:2023:i:c:s0047259x23000349
    DOI: 10.1016/j.jmva.2023.105188
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    References listed on IDEAS

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    1. 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).
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    3. Saâdaoui, Foued, 2010. "Acceleration of the EM algorithm via extrapolation methods: Review, comparison and new methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 750-766, March.
    4. Michael Cohen & Siddhartha R. Dalal & John W. Tukey, 1993. "Robust, Smoothly Heterogeneous Variance Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(2), pages 339-353, June.
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    6. Foued SaÂdaoui, 2012. "A probabilistic clustering method for US interest rate analysis," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 135-148, November.
    7. 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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