High Dimensional Semiparametric Gaussian Copula Graphical Models

Han Liu, Fang Han, Ming Yuan, John D. Lafferty, Larry A. Wasserman

Abstract: ing the 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 dierent estimators under both ideal and noisy settings. The proposed methods are then applied on a largescale genomic dataset to illustrate their empirical usefulness. The R package huge implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran.r-project.org/.