摘要: We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point view. start n-sample law P_C R^p and focus on disadvantageous case where n is smaller than p. To estimate graph conditional dependences P_C, we introduce collection candidate then select one them minimizing penalized empirical risk. Our main result assess performance procedure setting. pay special attention to maximal degree D that can handle, which turns be roughly n/(2 log p).
arxiv.org
128.84.21.199参考文章(17)
Fanny Villers, Brigitte Schaeffer, Caroline Bertin, Sylvie Huet, Assessing the Validity Domains of Graphical Gaussian Models in Order to Infer Relationships among Components of Complex Biological Systems Statistical Applications in Genetics and Molecular Biology. ,vol. 7, pp. 1- 37 ,(2008) , 10.2202/1544-6115.1371
Kenneth R. Davidson, Stanislaw J. Szarek, Chapter 8 - Local Operator Theory, Random Matrices and Banach Spaces Handbook of the Geometry of Banach Spaces. ,vol. 1, pp. 317- 366 ,(2001) , 10.1016/S1874-5849(01)80010-3
Alexandre d'Aspremont, Onureena Banerjee, Laurent El Ghaoui, Model Selection Through Sparse Maximum Likelihood Estimation arXiv: Artificial Intelligence. ,(2007)
Robert Tibshirani, Trevor Hastie, Jerome Friedman, Sparse inverse covariance estimation with the lasso arXiv: Methodology. ,(2007)
Mathias Drton, Michael D. Perlman, Multiple Testing and Error Control in Gaussian Graphical Model Selection Statistical Science. ,vol. 22, pp. 430- 449 ,(2007) , 10.1214/088342307000000113
Nicolai Meinshausen, Peter Bühlmann, High-dimensional graphs and variable selection with the Lasso Annals of Statistics. ,vol. 34, pp. 1436- 1462 ,(2006) , 10.1214/009053606000000281
Richard Baraniuk, Mark Davenport, Ronald DeVore, Michael Wakin, A Simple Proof of the Restricted Isometry Property for Random Matrices Constructive Approximation. ,vol. 28, pp. 253- 263 ,(2008) , 10.1007/S00365-007-9003-X
Yannick Baraud, Christophe Giraud, Sylvie Huet, Gaussian model selection with an unknown variance Annals of Statistics. ,vol. 37, pp. 630- 672 ,(2009) , 10.1214/07-AOS573
Jianhua Z. Huang, Naiping Liu, Mohsen Pourahmadi, Linxu Liu, Covariance matrix selection and estimation via penalised normal likelihood Biometrika. ,vol. 93, pp. 85- 98 ,(2006) , 10.1093/BIOMET/93.1.85
M. Yuan, Y. Lin, Model selection and estimation in the Gaussian graphical model Biometrika. ,vol. 94, pp. 19- 35 ,(2007) , 10.1093/BIOMET/ASM018