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.
Mots-clés : model-based clustering, variable selection, penalized likelihood criterion, bracketing entropy
@article{PS_2011__15__41_0,
author = {Maugis, Cathy and Michel, Bertrand},
title = {A non asymptotic penalized criterion for gaussian mixture model selection},
journal = {ESAIM: Probability and Statistics},
pages = {41--68},
publisher = {EDP-Sciences},
volume = {15},
year = {2011},
doi = {10.1051/ps/2009004},
mrnumber = {2870505},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2009004/}
}
TY - JOUR AU - Maugis, Cathy AU - Michel, Bertrand TI - A non asymptotic penalized criterion for gaussian mixture model selection JO - ESAIM: Probability and Statistics PY - 2011 SP - 41 EP - 68 VL - 15 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2009004/ DO - 10.1051/ps/2009004 LA - en ID - PS_2011__15__41_0 ER -
%0 Journal Article %A Maugis, Cathy %A Michel, Bertrand %T A non asymptotic penalized criterion for gaussian mixture model selection %J ESAIM: Probability and Statistics %D 2011 %P 41-68 %V 15 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2009004/ %R 10.1051/ps/2009004 %G en %F PS_2011__15__41_0
Maugis, Cathy; Michel, Bertrand. A non asymptotic penalized criterion for gaussian mixture model selection. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 41-68. doi : 10.1051/ps/2009004. http://archive.numdam.org/articles/10.1051/ps/2009004/
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