High Dimensional Semiparametric Gaussian Copula Graphical Models

作者：Han Liu, Fang Han, M. Yuan, J. Lafferty, L. Wasserman · 发表于：International Conference on Machine Learning · 年份：2012 · 被引用次数：234 · 研究领域：Computer Science、Mathematics

We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation, we exploit nonparametric rank-based correlation coefficient estimators including the 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 nonparanormal graphical models are a safe replacement of the Gaussian graphical models, even when the data are Gaussian.