Acceleration of the EM algorithm using the vector epsilon algorithm

Authors:
Mingfeng Wang;Masahiro Kuroda;Michio Sakakihara;Zhi Geng
Affiliations:
Institute of Mathematical Sciences, Peking University, Beijing, China 100871;Department of Socio-Information, Okayama University of Science, Okayama, Japan 700-0005;Department of Information Science, Okayama University of Science, Okayama, Japan 700-0005;Institute of Mathematical Sciences, Peking University, Beijing, China 100871
Venue:
Computational Statistics
Year:
2008

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Abstract

The expectation---maximization (EM) algorithm is a very general and popular iterative computational algorithm to find maximum likelihood estimates from incomplete data and broadly used to statistical analysis with missing data, because of its stability, flexibility and simplicity. However, it is often criticized that the convergence of the EM algorithm is slow. The various algorithms to accelerate the convergence of the EM algorithm have been proposed. The vector 驴 algorithm of Wynn (Math Comp 16:301---322, 1962) is used to accelerate the convergence of the EM algorithm in Kuroda and Sakakihara (Comput Stat Data Anal 51:1549---1561, 2006). In this paper, we provide the theoretical evaluation of the convergence of the 驴-accelerated EM algorithm. The 驴-accelerated EM algorithm does not use the information matrix but only uses the sequence of estimates obtained from iterations of the EM algorithm, and thus it keeps the flexibility and simplicity of the EM algorithm.