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MM Algorithms for Some Discrete Multivariate Distributions.

ABSTRACT: The MM (minorization-maximization) principle is a versatile tool for constructing optimization algorithms. Every EM algorithm is an MM algorithm but not vice versa. This article derives MM algorithms for maximum likelihood estimation with discrete multivariate distributions such as the Dirichlet-multinomial and Connor-Mosimann distributions, the Neerchal-Morel distribution, the negative-multinomial distribution, certain distributions on partitions, and zero-truncated and zero-inflated distributions. These MM algorithms increase the likelihood at each iteration and reliably converge to the maximum from well-chosen initial values. Because they involve no matrix inversion, the algorithms are especially pertinent to high-dimensional problems. To illustrate the performance of the MM algorithms, we compare them to Newton's method on data used to classify handwritten digits.

SUBMITTER: Zhou H

PROVIDER: S-EPMC2945396 | biostudies-literature | 2010 Sep

REPOSITORIES: biostudies-literature

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MM Algorithms for Some Discrete Multivariate Distributions.

Zhou Hua H Lange Kenneth K

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20100901 3

The MM (minorization-maximization) principle is a versatile tool for constructing optimization algorithms. Every EM algorithm is an MM algorithm but not vice versa. This article derives MM algorithms for maximum likelihood estimation with discrete multivariate distributions such as the Dirichlet-multinomial and Connor-Mosimann distributions, the Neerchal-Morel distribution, the negative-multinomial distribution, certain distributions on partitions, and zero-truncated and zero-inflated distributi ...[more]

PMID: 20877446

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