We consider the problem of estimating the conditional mean of a real gaussian variable Y=∑i=1pθiXi+ɛ where the vector of the covariates (Xi)1≤i≤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,...

We deal with the problem of choosing a piecewise constant estimator of a regression function s mapping $𝒳$ into $ℝ$. We consider a non Gaussian regression framework with deterministic design points, and we adopt the non asymptotic approach of model selection via penalization developed by Birgé and Massart. Given a collection of partitions of $𝒳$, with possibly exponential complexity, and the corresponding collection of piecewise constant estimators, we propose a penalized least squares criterion which...