Open Access
August 2012 High-dimensional semiparametric Gaussian copula graphical models
Han Liu, Fang Han, Ming Yuan, John Lafferty, Larry Wasserman
Ann. Statist. 40(4): 2293-2326 (August 2012). DOI: 10.1214/12-AOS1037


We propose a semiparametric approach called the nonparanormal SKEPTIC for efficiently and robustly estimating high-dimensional undirected graphical models. To achieve modeling flexibility, we consider the nonparanormal graphical models proposed by Liu, Lafferty and Wasserman [J. Mach. Learn. Res. 10 (2009) 2295–2328]. To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including Spearman’s rho and Kendall’s tau. We prove that the nonparanormal SKEPTIC achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation. This result suggests that the nonparanormal graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian. Besides theoretical analysis, we also conduct thorough numerical simulations to compare the graph recovery performance of different estimators under both ideal and noisy settings. The proposed methods are then applied on a large-scale genomic data set to illustrate their empirical usefulness. The R package huge implementing the proposed methods is available on the Comprehensive R Archive Network:


Download Citation

Han Liu. Fang Han. Ming Yuan. John Lafferty. Larry Wasserman. "High-dimensional semiparametric Gaussian copula graphical models." Ann. Statist. 40 (4) 2293 - 2326, August 2012.


Published: August 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1297.62073
MathSciNet: MR3059084
Digital Object Identifier: 10.1214/12-AOS1037

Primary: 62G05
Secondary: 62F12 , 62G20

Keywords: biological regulatory networks , Gaussian copula , High-dimensional statistics , Minimax optimality , nonparanormal graphical models , robust statistics , undirected graphical models

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 4 • August 2012
Back to Top