Conditional Density Estimation by Penalized Likelihood Model Selection and Applications

Serge Cohen 1 Erwan Le Pennec 2, 3, *
* Auteur correspondant
2 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a Kullback-Leibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a best model within a collection. We give a general condition on penalty choice that leads to oracle type inequality for the resulting estimate. This construction is applied to two examples of partition-based conditional density models, models in which the conditional density depends only in a piecewise manner from the covariate. The first example relies on classical piecewise polynomial densities while the second uses Gaussian mixtures with varying mixing proportion but same mixture components. We show how this last case is related to an unsupervised segmentation application that has been the source of our motivation to this study.
Type de document :
Rapport
[Research Report] RR-7596, 2011
Liste complète des métadonnées

Littérature citée [52 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00575462
Contributeur : Erwan Le Pennec <>
Soumis le : lundi 9 juillet 2012 - 13:33:03
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14
Document(s) archivé(s) le : jeudi 15 décembre 2016 - 21:07:29

Fichiers

ConditionalDensityPreprint.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : inria-00575462, version 5
  • ARXIV : 1103.2021

Citation

Serge Cohen, Erwan Le Pennec. Conditional Density Estimation by Penalized Likelihood Model Selection and Applications. [Research Report] RR-7596, 2011. 〈inria-00575462v5〉

Partager

Métriques

Consultations de la notice

305

Téléchargements de fichiers

125