The MM Alternative to EM

Details The MM Alternative to EM The MM Alternative to EM

2011-04-12

arxiv.org/abs/1104.2203v1

Statistical Science 2010, Vol. 25, No. 4, 492-505

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/08-STS264 the Statistical Science (http://www.imstat.org/sts/) by the Institute of M

Scientific paper

10.1214/08-STS264

The EM algorithm is a special case of a more general algorithm called the MM algorithm. Specific MM algorithms often have nothing to do with missing data. The first M step of an MM algorithm creates a surrogate function that is optimized in the second M step. In minimization, MM stands for majorize--minimize; in maximization, it stands for minorize--maximize. This two-step process always drives the objective function in the right direction. Construction of MM algorithms relies on recognizing and manipulating inequalities rather than calculating conditional expectations. This survey walks the reader through the construction of several specific MM algorithms. The potential of the MM algorithm in solving high-dimensional optimization and estimation problems is its most attractive feature. Our applications to random graph models, discriminant analysis and image restoration showcase this ability.

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