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Damped Anderson Acceleration With restarts and Monotonicity Control for Accelerating EM and EM-like algorithms (10.1080/10618600.2019.1594835, 2019)

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2019年第4期28卷 I-I页

作者： Henderson, Nicholas C. Varadhan, Ravi Sidney Kimmel Comprehensive Cancer Center Johns Hopkins University Baltimore MD Sidney Kimmel Comprehensive Cancer Center Johns Hopkins University Baltimore MD Department of Biostatistics Bloomberg School of Public Health Johns Hopkins University Baltimore MD

The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates in a variety of statistical problems. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed slow convergence which often hinders the application of EM algorithms in high-dimensional problems or in other complex settings. To address the need for more rapidly convergent EM algorithms, we describe a new class of acceleration schemes that build on the Anderson acceleration technique for speeding fixed-point iterations. Our approach is effective at greatly accelerating the convergence of EM algorithms and is automatically scalable to high-dimensional settings. Through the introduction of periodic algorithm restarts and a damping factor, our acceleration scheme provides faster and more robust convergence when compared to un-modified Anderson acceleration, while also improving global convergence. Crucially, our method works as an “off-the-shelf” method in that it may be directly used to accelerate any EM algorithm without relying on the use of any model-specific features or insights. Through a series of simulation studies involving five representative problems, we show that our algorithm is substantially faster than the existing state-of-art acceleration schemes. The acceleration schemes described in this paper are implemented in the R package daarem which is available from the comprehensive R archive network (https://***). Supplementary materials for this article are available online.

关键词： algorithm restarts Convergence acceleration MM algorithm Quasi-Newton SQUAREM

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