# General A Tutorial on MM Algorithms

@inproceedings{Ange2007GeneralAT, title={General A Tutorial on MM Algorithms}, author={Kenneth L Ange}, year={2007} }

Most problems in frequentist statistics involve optimization of a function such as a likelihood or a sum of squares. EM algorithms are among the most effective algorithms for maximum likelihood estimation because they consistently drive the likelihood uphill by maximizing a simple surrogate function for the log-likelihood. Iterative optimization of a surrogate function as exempli ed by an EM algorithm does not necessarily require missing data. Indeed, every EM algorithm is a special case of…

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Because optimization transfer algorithms often exhibit the slow convergence of EM algorithms, two methods of accelerating optimization transfer are discussed and evaluated in the context of specific problems.

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A connection is established between local quadratic approximation and the so-called MM algorithms, useful extensions of the EM algorithms, to analyze the local and global convergence of the local quadRatic approximation algorithm by employing the techniques used for EM algorithms.

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Preliminary numerical testing of the algorithms on simulated data suggest that the convex algorithm and the ad hoc gradient algorithm are computationally superior to the EM algorithm.

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It is desirable that a numerical maximization algorithm monotonically increase its objective function for the sake of its stability of convergence. It is here shown how one can adjust the…

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The new method is a natural extension of the EM for maximizing likelihood with concave priors for emission tomography and convergence proofs are given.