  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.
