Estimation of Gaussian graphs by model selection

Christophe Giraud (1, 2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 Unité MIAJ - INRA - Mathématiques et Informatique Appliquées

We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of P_C , we 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/(2 log p).

Mots clés: Gaussian Graphical Model; Random matrices; Model selection; Penalized empirical risk; gene regulation networks

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Giraud. Estimation of Gaussian graphs by model selection. Electronic Journal of Statistics , 2008, 2, pp.542--563. ⟨10.1214/08-EJS228⟩. ⟨hal-00178275v3⟩