Volume 12, April 2008
|Page(s)||308 - 326|
|Published online||08 May 2008|
On EM algorithms and their proximal generalizations
Université de Franche-Comté,
Laboratoire de Mathématiques, UMR CNRS 6623, 16 route de Gray, 25030 Besançon, France; firstname.lastname@example.org
2 Department of Electrical Engineering and Computer Science, 1301 Beal St., University of Michigan, Ann Arbor, MI 48109-2122, USA; email@example.com
Revised: 27 June 2007
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.
Mathematics Subject Classification: 65C20 / 65C60
Key words: Maximum Likelihood Estimation (MLE) / EM algorithm / proximal point algorithm / Karush-Kuhn-Tucker condition / mixture densities / competing risks models
© EDP Sciences, SMAI, 2008
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