Estimation of Gaussian graphs by model selection

Description

Our aim in this paper is to investigate Gaussian graph estimation from a theoretical and non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and we focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of P_C, we propose to introduce a collection of candidate graphs and then select one of them by minimizing a penalized empirical risk. Our main result assess the performance of the procedure in a non-asymptotic setting. We pay a special attention to the maximal degree D of the graphs that we can handle, which turns to be roughly n/(2log p).

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