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A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm.

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A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm. / Fearnhead, P.
In: Journal of Computational and Graphical Statistics, Vol. 13, No. 3, 01.09.2004, p. 739-750.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Fearnhead, P 2004, 'A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm.', Journal of Computational and Graphical Statistics, vol. 13, no. 3, pp. 739-750. https://doi.org/10.1198/106186004X2570

APA

Fearnhead, P. (2004). A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm. Journal of Computational and Graphical Statistics, 13(3), 739-750. https://doi.org/10.1198/106186004X2570

Vancouver

Fearnhead P. A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm. Journal of Computational and Graphical Statistics. 2004 Sept 1;13(3):739-750. doi: 10.1198/106186004X2570

Author

Fearnhead, P. / A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm. In: Journal of Computational and Graphical Statistics. 2004 ; Vol. 13, No. 3. pp. 739-750.

Bibtex

@article{bddaf4543b734f4895da8f424e445059,
title = "A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm.",
abstract = "This article considers a new approximation to the log-likelihood surface in mixture models. This approximation is based on both the mean and variance of the full-data loglikelihood over imputations of assignments of observations to components. This approximation is accurate to second order, and holds for general missing data problems. The approximation provides a new method for calculating the observed information using the EM algorithm, and motivates a Gauss-Newton method for finding the MLE. This GaussNewton method is implemented together with the ideas behind the SAGE algorithm. The resulting algorithm outperforms the EM, CEMM, and a further Gauss-Newton algorithm when analyzing data from three-component Gaussian mixtures.",
keywords = "CEMM, GAUSS-NEWTON, OBSERVED INFORMATION, SAGE",
author = "P. Fearnhead",
year = "2004",
month = sep,
day = "1",
doi = "10.1198/106186004X2570",
language = "English",
volume = "13",
pages = "739--750",
journal = "Journal of Computational and Graphical Statistics",
issn = "1537-2715",
publisher = "American Statistical Association",
number = "3",

}

RIS

TY - JOUR

T1 - A second order approximation to the log-likelihood surface for mixture models, with application to the EM algorithm.

AU - Fearnhead, P.

PY - 2004/9/1

Y1 - 2004/9/1

N2 - This article considers a new approximation to the log-likelihood surface in mixture models. This approximation is based on both the mean and variance of the full-data loglikelihood over imputations of assignments of observations to components. This approximation is accurate to second order, and holds for general missing data problems. The approximation provides a new method for calculating the observed information using the EM algorithm, and motivates a Gauss-Newton method for finding the MLE. This GaussNewton method is implemented together with the ideas behind the SAGE algorithm. The resulting algorithm outperforms the EM, CEMM, and a further Gauss-Newton algorithm when analyzing data from three-component Gaussian mixtures.

AB - This article considers a new approximation to the log-likelihood surface in mixture models. This approximation is based on both the mean and variance of the full-data loglikelihood over imputations of assignments of observations to components. This approximation is accurate to second order, and holds for general missing data problems. The approximation provides a new method for calculating the observed information using the EM algorithm, and motivates a Gauss-Newton method for finding the MLE. This GaussNewton method is implemented together with the ideas behind the SAGE algorithm. The resulting algorithm outperforms the EM, CEMM, and a further Gauss-Newton algorithm when analyzing data from three-component Gaussian mixtures.

KW - CEMM

KW - GAUSS-NEWTON

KW - OBSERVED INFORMATION

KW - SAGE

U2 - 10.1198/106186004X2570

DO - 10.1198/106186004X2570

M3 - Journal article

VL - 13

SP - 739

EP - 750

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1537-2715

IS - 3

ER -