The EM Algorithm, Its Randomized Implementation and Global Optimization: Some Challenges and Opportunities for Operations Research

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Summary

The EM algorithm is a very powerful optimization method and has become popular in many fields. Unfortunately, EM is only a local optimization method and can get stuck in sub-optimal solutions. While more and more contemporary data/model combinations yield multiple local optima, there have been only very few attempts at making EM suitable for global optimization. In this paper we review the basic EM algorithm, its properties and challenges, and we focus in particular on its randomized implementation. The randomized EM implementation promises to solve some of the contemporary data/model challenges, and it is particularly well-suited for a wedding with global optimization ideas, since most global optimization paradigms are also based on the principles of randomization. We review some of the challenges of the randomized EM implementation and present a new algorithm that combines the principles of EM with that of the Genetic Algorithm. While this new algorithm shows some promising results for clustering of an online auction database of functional objects, the primary goal of this work is to bridge a gap between the field of statistics, which is home to extensive research on the EM algorithm, and the field of operations research, in which work on global optimization thrives, and to stimulate new ideas for joint research between the two.