A non asymptotic penalized criterion for gaussian mixture model selection
ESAIM: Probability and Statistics, Volume 15 (2011), pp. 41-68.

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.

DOI: 10.1051/ps/2009004
Classification: 62H30,  62G07
Keywords: model-based clustering, variable selection, penalized likelihood criterion, bracketing entropy
     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},
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     year = {2011},
     doi = {10.1051/ps/2009004},
     mrnumber = {2870505},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2009004/}
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Maugis, Cathy; Michel, Bertrand. A non asymptotic penalized criterion for gaussian mixture model selection. ESAIM: Probability and Statistics, Volume 15 (2011), pp. 41-68. doi : 10.1051/ps/2009004. http://www.numdam.org/articles/10.1051/ps/2009004/

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