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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.
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TL;DR: It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation and some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.
Abstract: log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM algorithm in seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.
104 citations
TL;DR: In this paper, the authors discuss five questions concerning maximum likelihood estimation: What kind of theory is maximum likelihood, how it is used in practice, to what extent can this theory and practice be justified from a decision-theoretic viewpoint, what are maximum likelihood's principal virtues and defects, and what improvements have been suggested by decision theory.
Abstract: This paper discusses five questions concerning maximum likelihood estimation: What kind of theory is maximum likelihood? How is maximum likelihood used in practice? To what extent can this theory and practice be justified from a decision-theoretic viewpoint? What are maximum likelihood's principal virtues and defects? What improvements have been suggested by decision theory?
104 citations
TL;DR: Parsimonious skew- t and skew-normal analogues of the GPCM family that employ an eigenvalue decomposition of a scale matrix are introduced and are compared to existing models in both unsupervised and semi-supervised classification frameworks.
103 citations
TL;DR: In this article, the intractable expectations needed in the e −step can be written out analytically, bypassing the need for numerical estimation procedures, such as Monte Carlo methods, leading to accurate calculation of maximum likelihood estimates.
103 citations
TL;DR: A frequency-domain analysis of the expectation-maximization algorithm for maximum-likelihood image estimation that shows how the algorithm achieves this band extrapolation and gives the theoretical absolute bandwidth of the restored image.
Abstract: Computational optical-sectioning microscopy with a nonconfocal microscope is fundamentally limited because the optical transfer function, the Fourier transform of the point-spread function, is exactly zero over a conic region of the spatial-frequency domain. Because of this missing cone of optical information, images are potentially artifactual. To overcome this limitation, superresolution, in the sense of band extrapolation, is necessary. I present a frequency-domain analysis of the expectation-maximization algorithm for maximum-likelihood image estimation that shows how the algorithm achieves this band extrapolation. This analysis gives the theoretical absolute bandwidth of the restored image; however, this absolute value may not be realistic in many cases. Then a second analysis is presented that assumes a Gaussian point-spread function and a specimen function and shows more realistic behavior of the algorithm and demonstrates some of its properties. Experimental results on the superresolving capability of the algorithm are also presented.
103 citations