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