hal-00178275, version 1
Estimation of Gaussian graphs by model selection
Abstract: 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/(2 log p).
- 1:
- CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
- 2:
- Institut national de la recherche agronomique (INRA) : UR341
- Domain : Mathematics/Statistics
- Keywords : Gaussian graphs – Random matrices – Model selection – Penalized criterion
- Comment : 17 pages
- Available versions : v1 (2007-10-10) v2 (2008-04-18) v3 (2008-07-16)
- hal-00178275, version 1
- http://hal.archives-ouvertes.fr/hal-00178275
- oai:hal.archives-ouvertes.fr:hal-00178275
- From:
- Submitted on: Wednesday, 10 October 2007 15:42:01
- Updated on: Wednesday, 10 October 2007 17:36:49
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