# A non asymptotic penalized criterion for gaussian mixture model selection

ESAIM: Probability and Statistics (2011)

- Volume: 15, page 41-68
- ISSN: 1292-8100

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topMaugis, Cathy, and Michel, Bertrand. "A non asymptotic penalized criterion for gaussian mixture model selection." ESAIM: Probability and Statistics 15 (2011): 41-68. <http://eudml.org/doc/277155>.

@article{Maugis2011,

abstract = {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.},

author = {Maugis, Cathy, Michel, Bertrand},

journal = {ESAIM: Probability and Statistics},

keywords = {model-based clustering; variable selection; penalized likelihood criterion; bracketing entropy},

language = {eng},

pages = {41-68},

publisher = {EDP-Sciences},

title = {A non asymptotic penalized criterion for gaussian mixture model selection},

url = {http://eudml.org/doc/277155},

volume = {15},

year = {2011},

}

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

PB - EDP-Sciences

VL - 15

SP - 41

EP - 68

AB - 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.

LA - eng

KW - model-based clustering; variable selection; penalized likelihood criterion; bracketing entropy

UR - http://eudml.org/doc/277155

ER -

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## Citations in EuDML Documents

top- Caroline Meynet, An ℓ1-oracle inequality for the Lasso in finite mixture gaussian regression models
- C. Maugis-Rabusseau, B. Michel, Adaptive density estimation for clustering with gaussian mixtures
- Cathy Maugis, Bertrand Michel, Data-driven penalty calibration: A case study for gaussian mixture model selection
- Cathy Maugis, Bertrand Michel, Data-driven penalty calibration: A case study for Gaussian mixture model selection
- Yannick Baraud, Lucien Birgé, Estimating composite functions by model selection

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