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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