High-dimensional Gaussian model selection on a Gaussian design

Nicolas Verzelen 1, 2
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 : We consider the problem of estimating the conditional mean of a real Gaussian variable $\nolinebreak Y=\sum_{i=1}^p\nolinebreak\theta_iX_i+\nolinebreak \epsilon$ where the vector of the covariates $(X_i)_{1\leq i\leq p}$ follows a joint Gaussian distribution. This issue often occurs when one aims at estimating the graph or the distribution of a Gaussian graphical model. We introduce a general model selection procedure which is based on the minimization of a penalized least-squares type criterion. It handles a variety of problems such as ordered and complete variable selection, allows to incorporate some prior knowledge on the model and applies when the number of covariates $p$ is larger than the number of observations $n$. Moreover, it is shown to achieve a non-asymptotic oracle inequality independently of the correlation structure of the covariates. We also exhibit various minimax rates of estimation in the considered framework and hence derive adaptiveness properties of our procedure.
Type de document :
Pré-publication, Document de travail
RR-6616. 2008
Liste complète des métadonnées

https://hal.inria.fr/inria-00311412
Contributeur : Nicolas Verzelen <>
Soumis le : mardi 28 avril 2009 - 10:48:34
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:55:24

Fichiers

RR-oracle.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : inria-00311412, version 2
  • ARXIV : 0808.2152

Collections

Citation

Nicolas Verzelen. High-dimensional Gaussian model selection on a Gaussian design. RR-6616. 2008. 〈inria-00311412v2〉

Partager

Métriques

Consultations de la notice

246

Téléchargements de fichiers

128