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Expectation–maximization algorithm

About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.


Papers
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Journal ArticleDOI
TL;DR: The EM algorithm, a convenient method for computing maximum likelihood estimates in missing-data problems, is described and applied to two common models, the multivariate normal model for continuous data and the multinomial model for discrete data.
Abstract: Methods for handling missing data in social science data sets are reviewed. Limitations of common practical approaches, including complete-case analysis, available-case analysis and imputation, are illustrated on a simple missing-data problem with one complete and one incomplete variable. Two more principled approaches, namely maximum likelihood under a model for the data and missing-data mechanism and multiple imputation, are applied to the bivariate problem. General properties of these methods are outlined, and applications to more complex missing-data problems are discussed. The EM algorithm, a convenient method for computing maximum likelihood estimates in missing-data problems, is described and applied to two common models, the multivariate normal model for continuous data and the multinomial model for discrete data. Multiple imputation under explicit or implicit models is recommended as a method that retains the advantages of imputation and overcomes its limitations.

994 citations

Journal ArticleDOI
TL;DR: The maximum likelihood method is described and how likelihood ratio tests of a variety of biological hypotheses can be formulated and tested using computer simulation to generate the null distribution of the likelihood ratio test statistic is described.
Abstract: One of the strengths of the maximum likelihood method of phylogenetic estimation is the ease with which hypotheses can be formulated and tested. Maximum likelihood analysis of DNA and amino acid sequence data has been made practical with recent advances in models of DNA substitution, computer programs, and computational speed. Here, we describe the maximum likelihood method and the recent improvements in models of substitution. We also describe how likelihood ratio tests of a variety of biological hypotheses can be formulated and tested using computer simulation to generate the null distribution of the likelihood ratio test statistic.

967 citations

Journal ArticleDOI
TL;DR: In this paper, the application of the GHK simulation method for maximum likelihood estimation of the multivariate probit regression model is discussed, and a Stata program mvprobit is described.
Abstract: We discuss the application of the GHK simulation method for maximum likelihood estimation of the multivariate probit regression model and describe and illustrate a Stata program mvprobit for this purpose.

962 citations

Journal ArticleDOI
TL;DR: In this article, a comprehensive, non-technical overview of the three maximum likelihood algorithms is provided. But, confusion appears to exist over the differences among the three algorithms, and they belong to the same family of estimators.
Abstract: Maximum likelihood algorithms for use with missing data are becoming commonplace in microcomputer packages. Specifically, 3 maximum likelihood algorithms are currently available in existing software packages: the multiple-group approach, full information maximum likelihood estimation, and the EM algorithm. Although they belong to the same family of estimator, confusion appears to exist over the differences among the 3 algorithms. This article provides a comprehensive, nontechnical overview of the 3 maximum likelihood algorithms. Multiple imputation, which is frequently used in conjunction with the EM algorithm, is also discussed.

956 citations

Proceedings ArticleDOI
07 Apr 1986
TL;DR: A method for estimating the parameters of hidden Markov models of speech is described and recognition results are presented comparing this method with maximum likelihood estimation.
Abstract: A method for estimating the parameters of hidden Markov models of speech is described. Parameter values are chosen to maximize the mutual information between an acoustic observation sequence and the corresponding word sequence. Recognition results are presented comparing this method with maximum likelihood estimation.

921 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023114
2022245
2021438
2020410
2019484
2018519