Issue |
ESAIM: PS
Volume 15, 2011
|
|
---|---|---|
Page(s) | 41 - 68 | |
DOI | https://doi.org/10.1051/ps/2009004 | |
Published online | 05 January 2012 |
A non asymptotic penalized criterion for Gaussian mixture model selection
1
Institut de Mathématiques de Toulouse, INSA de Toulouse, Université de Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France; cathy.maugis@insa-toulouse.fr
2
Laboratoire de Statistique Théorique et Appliquée, Université Paris 6, 175 rue du Chevaleret, 75013 Paris, France; bertrand.michel@upmc.fr
Received:
19
September
2008
Revised:
13
February
2009
Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour, July 6–23 (2003)] is used to obtain the penalty function form. This theorem requires to control the bracketing entropy of Gaussian mixture families. The ordered and non-ordered variable selection cases are both addressed in this paper.
Mathematics Subject Classification: 62H30 / 62G07
Key words: Model-based clustering / variable selection / penalized likelihood criterion / bracketing entropy
© EDP Sciences, SMAI, 2011
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