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On EM algorithms and their proximal generalizations

Published online by Cambridge University Press:  08 May 2008

Stéphane Chrétien  and
Alfred O. Hero
Stéphane Chrétien
Affiliation:
Université de Franche-Comté, Laboratoire de Mathématiques, UMR CNRS 6623, 16 route de Gray, 25030 Besançon, France; [email protected]
Alfred O. Hero
Affiliation:
Department of Electrical Engineering and Computer Science, 1301 Beal St., University of Michigan, Ann Arbor, MI 48109-2122, USA; [email protected]
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Abstract

In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [Chretien and Hero (1998)] and called Kullback-proximal algorithms. The proximal framework allows us to prove new results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space.

Keywords

Maximum Likelihood Estimation (MLE)EM algorithmproximal point algorithmKarush-Kuhn-Tucker conditionmixture densitiescompeting risks models
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 308 - 326
Copyright
© EDP Sciences, SMAI, 2008

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