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Acceleration of the EM algorithm via extrapolation methods: Review, comparison and new methods

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  • Saâdaoui, Foued

Abstract

EM-type algorithms are popular tools for modal estimation and the most widely used parameter estimation procedures in statistical modeling. However, they are often criticized for their slow convergence. Despite the appearance of numerous acceleration techniques along the last decades, their use has been limited because they are either difficult to implement or not general. In the present paper, a new generation of fast, general and simple maximum likelihood estimation (MLE) algorithms is presented. In these cyclic iterative algorithms, extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. Some new complementary strategies like cycling, squaring and alternating are added to that processes. The presented schemes generally exhibit either fast-linear or superlinear convergence. Numerical illustrations allow us to compare a selection of its variants and generally confirm that this category is extremely simple as well as fast.

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  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:3:p:750-766
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    References listed on IDEAS

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    1. 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.
    2. Berlinet, A. & Roland, Ch., 2007. "Acceleration schemes with application to the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3689-3702, May.
    3. 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.
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    Cited by:

    1. Saâdaoui, Foued, 2023. "Skewed multifractal scaling of stock markets during the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Saâdaoui, Foued, 2023. "Randomized extrapolation for accelerating EM-type fixed-point algorithms," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    3. Foued Saâdaoui & Hana Rabbouch, 2024. "Structured multifractal scaling of the principal cryptocurrencies: Examination using a self‐explainable machine learning," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(7), pages 2917-2934, November.
    4. Saâdaoui, Foued & Ben Jabeur, Sami, 2023. "Analyzing the influence of geopolitical risks on European power prices using a multiresolution causal neural network," Energy Economics, Elsevier, vol. 124(C).

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