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Partition-based conditional density estimation

Published online by Cambridge University Press:  04 November 2013

S. X. Cohen  and
E. Le Pennec
S. X. Cohen
Affiliation:
IPANEMA USR 3461 CNRS/MCC, BP 48 Saint Aubin, F-91192 Gif-sur-Yvette, France
E. Le Pennec
Affiliation:
SELECT/Inria Saclay IdF, Laboratoire de Mathématiques Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, France. Erwan.LePennec@inria.fr
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Abstract

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 classical strategy in which the densities are chosen piecewise conditional according to the variable. We then consider Gaussian mixture models with mixing proportion that vary according to the covariate but with common mixture components. This model proves to be interesting for an unsupervised segmentation application that was our original motivation for this work.

Keywords

Conditional density estimationpartitionpenalized likelihoodpiecewise polynomial densityGaussian mixture model
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 672 - 697
Copyright
© EDP Sciences, SMAI, 2013

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