HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

High-dimensional Gaussian model selection on a Gaussian design

Nicolas Verzelen 1, 2
2 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Contributor : Nicolas Verzelen Connect in order to contact the contributor
Submitted on : Tuesday, April 28, 2009 - 10:48:34 AM
Last modification on : Tuesday, July 6, 2021 - 3:39:45 AM
Long-term archiving on: : Wednesday, September 22, 2010 - 12:55:24 PM


Files produced by the author(s)


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


Nicolas Verzelen. High-dimensional Gaussian model selection on a Gaussian design. 2008. ⟨inria-00311412v2⟩



Record views


Files downloads