Displaying similar documents to “A non asymptotic penalized criterion for gaussian mixture model selection”

A non asymptotic penalized criterion for Gaussian mixture model selection

Cathy Maugis, Bertrand Michel (2012)

ESAIM: Probability and Statistics

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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  Springer, Berlin (2007). Lectures from the 33rd Summer School on...

Data-driven penalty calibration: A case study for gaussian mixture model selection

Cathy Maugis, Bertrand Michel (2011)

ESAIM: Probability and Statistics

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In the companion paper [C. Maugis and B. Michel, A non asymptotic penalized criterion for Gaussian mixture model selection. 15 (2011) 41–68] , a penalized likelihood criterion is proposed to select a Gaussian mixture model among a specific model collection. This criterion depends on unknown constants which have to be calibrated in practical situations. A “slope heuristics” method is described and experimented to deal with this practical problem. In a model-based clustering context,...

Data-driven penalty calibration: A case study for Gaussian mixture model selection

Cathy Maugis, Bertrand Michel (2012)

ESAIM: Probability and Statistics

Similarity:

In the companion paper [C. Maugis and B. Michel, A non asymptotic penalized criterion for Gaussian mixture model selection. (2011) 41–68] , a penalized likelihood criterion is proposed to select a Gaussian mixture model among a specific model collection. This criterion depends on unknown constants which have to be calibrated in practical situations. A “slope heuristics” method is described and experimented to deal with this practical problem. In a model-based clustering...

Adaptive density estimation for clustering with gaussian mixtures

C. Maugis-Rabusseau, B. Michel (2013)

ESAIM: Probability and Statistics

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Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum likelihood estimator is proposed for automatically selecting the number of mixture components. In the present paper, a collection of univariate densities whose logarithm is locally -Hölder with moment and tail conditions are considered. We show that this...

Partition-based conditional density estimation

S. X. Cohen, E. Le Pennec (2013)

ESAIM: Probability and Statistics

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We propose a general partition-based strategy to estimate conditional density with candidate densities that are piecewise constant with respect to the covariate. Capitalizing on a general penalized maximum likelihood model selection result, we prove, on two specific examples, that the penalty of each model can be chosen roughly proportional to its dimension. We first study a strategy in which the densities are chosen piecewise conditional according to the variable. We then consider Gaussian...

An ℓ1-oracle inequality for the Lasso in finite mixture gaussian regression models

Caroline Meynet (2013)

ESAIM: Probability and Statistics

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We consider a finite mixture of Gaussian regression models for high-dimensional heterogeneous data where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by an -penalized maximum likelihood estimator. We shall provide an -oracle inequality satisfied by this Lasso estimator with the Kullback–Leibler loss. In particular, we give a condition on the regularization parameter of...