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hal-00178275, version 2

Estimation of Gaussian graphs by model selection

Christophe Giraud () 1, 2

Abstract: 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).

  • 1:  Laboratoire Jean Alexandre Dieudonné (JAD)
  • CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
  • 2:  Mathématiques et Informatique Appliquées - Jouy en Josas (MIAJ)
  • Institut national de la recherche agronomique (INRA) : UR341
  • Domain : Mathematics/Statistics
    Statistics/Statistics Theory
  • Keywords : Gaussian Graphical Model – Random matrices – Model selection – Penalized empirical risk – gene regulation networks
  • Comment : 21 pages
  • Available versions :  v1 (2007-10-10) v2 (2008-04-18) v3 (2008-07-16)
 
  • hal-00178275, version 2
  • http://hal.archives-ouvertes.fr/hal-00178275
  • oai:hal.archives-ouvertes.fr:hal-00178275
  • From: Christophe Giraud <>
  • Submitted on: Thursday, 17 April 2008 22:05:26
  • Updated on: Friday, 18 April 2008 06:26:11