We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from an n-sample of a Gaussian law ℙC in ℝp and focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of ℙC, we introduce a collection of candidate graphs and then select one of them by minimizing a penalized empirical risk. Our main result assesses the performance of the procedure in a non-asymptotic setting. We pay special attention to the maximal degree D of the graphs that we can handle, which turns to be roughly n/(2logp).
"Estimation of Gaussian graphs by model selection." Electron. J. Statist. 2 542 - 563, 2008. https://doi.org/10.1214/08-EJS228