The Em Algorithm And Extensions Pdf

the em algorithm and extensions pdf

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Moreover, ecme can have a substantially faster convergence rate than either EM or ECM, measured using either the number of iterations or actual computer time. There are two reasons for this improvement. Secondly, ecme allows faster converging numerical methods to be used on only those constrained maximisations where they are most efficacious.

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In statistics , an expectation—maximization EM algorithm is an iterative method to find local maximum likelihood or maximum a posteriori MAP estimates of parameters in statistical models , where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation E step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization M step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step.

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Moreover, ecme can have a substantially faster convergence rate than either EM or ECM, measured using either the number of iterations or actual computer time. There are two reasons for this improvement.

Secondly, ecme allows faster converging numerical methods to be used on only those constrained maximisations where they are most efficacious. Illustrative ecme algorithms are presented with both closed-form and iterative CM-steps, which demonstrate the faster rate of convergence and the associated easier assessment of convergence.

Also, theoretical expressions are presented and illustrated regarding the rate of convergence of ecme. Finally, relationships with Markov chain Monte Carlo methods are discussed. Most users should sign in with their email address. If you originally registered with a username please use that to sign in. To purchase short term access, please sign in to your Oxford Academic account above.

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The EM Algorithm and Extensions (eBook)

Complete with updates that capture developments from the past decade, The EM Algorithm and Extensions, Second Edition successfully provides a basic understanding of the EM algorithm by describing its inception, implementation, and applicability in numerous statistical contexts. In conjunction with the fundamentals of the topic, the authors discuss convergence issues and computation of standard errors, and, in addition, unveil many parallels and connections between the EM algorithm and Markov chain Monte Carlo algorithms. Thorough discussions on the complexities and drawbacks that arise from the basic EM algorithm, such as slow convergence and lack of an in-built procedure to compute the covariance matrix of parameter estimates, are also presented. While the general philosophy of the First Edition has been maintained, this timely new edition has been updated, revised, and expanded to include:. New results on convergence, including convergence of the EM algorithm in constrained parameter spaces. Expanded discussion of standard error computation methods, such as methods for categorical data and methods based on numerical differentiation.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: McLachlan and T. McLachlan , T.

Expectation–maximization algorithm

Complete with updates that capture developments from the past decade, The EM Algorithm and Extensions, Second Edition successfully provides a basic understanding of the EM algorithm by describing its inception, implementation, and applicability in numerous statistical contexts. In conjunction with the fundamentals of the topic, the authors discuss convergence issues and computation of standard errors, and, in addition, unveil many parallels and connections between the EM algorithm and Markov chain Monte Carlo algorithms. Thorough discussions on the complexities and drawbacks that arise from the basic EM algorithm, such as slow convergence and lack of an in-built procedure to compute the covariance matrix of parameter estimates, are also presented. While the general philosophy of the First Edition has been maintained, this timely new edition has been updated, revised, and expanded to include:.

The EM Algorithm and Extensions.pdf

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The EM algorithm and extensions

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