The Nonparanormal Skeptic

• Activity Number: 168
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Han Liu*+
• Companies: The Johns Hopkins University
• Keywords: high dimensional statistics ; graphical models ; Gausian copula ; robust statistics ; minimax optimality ; biological regulatory networks

Abstract

We propose a semiparametric approach, named nonparanormal SKEPTIC, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models ( or the nonparanromal models as proposed by Liu et al. (2009)). To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including Spearman's rho and Kendall's tau. In high dimensional settings, we prove that the nonparanormal SKEPTIC achieves the optimal parametric rate of convergence in both graph and parameter estimation. This result suggests that the Gaussian copula 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 different estimators for their graph recovery performance under both ideal and noisy settings.