| Issue |
ESAIM: PS
Volume 12, April 2008
|
|
|---|---|---|
| Page(s) | 308 - 326 | |
| DOI | https://doi.org/10.1051/ps:2007041 | |
| Published online | 08 May 2008 | |
On EM algorithms and their proximal generalizations
1
Université de Franche-Comté,
Laboratoire de Mathématiques, UMR CNRS 6623, 16 route de Gray, 25030 Besançon, France; chretien@math.univ-fcomte.fr
2
Department of Electrical Engineering and Computer Science, 1301 Beal St., University of Michigan, Ann Arbor, MI 48109-2122, USA; hero@eecs.umich.edu
Received:
14
June
2007
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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