HIGH-DIMENSIONAL SEMIPARAMETRIC GAUSSIAN COPULA GRAPHICAL MODELS

• 成果类型: Article
• 署名作者: Liu, Han; Han, Fang; Yuan, Ming; Lafferty, John; Wasserman, Larry
• 署名单位: Princeton University; Johns Hopkins University; Johns Hopkins Bloomberg School of Public Health; University System of Georgia; Georgia Institute of Technology; University of Chicago; Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1037
• 发表日期: 2012
• 页码: 2293-2326
• 关键词: selection; maximum

摘要

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: http://cran.r-project.org/.