HIGH-DIMENSIONAL SEMIPARAMETRIC GAUSSIAN COPULA GRAPHICAL MODELS
HIGH-DIMENSIONAL SEMIPARAMETRIC GAUSSIAN COPULA GRAPHICAL MODELS
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DOI：
10.1214/12-aos1037
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发表时间：
2012-08-01
影响因子：
4.5
通讯作者：
Wasserman, Larry
中科院分区：
文献类型：
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作者：
Liu, Han;Han, Fang;Wasserman, Larry
我们提出了一种半参数方法，称为非政治怀疑论者，以有效且可靠地估计高维无向图形模型。为了实现建模灵活性，我们考虑了Liu，Lafferty和Wasserman提出的非政治图形模型[J.马赫。学习。 res。 10（2009）2295-2328]。为了实现估计鲁棒性，我们利用了基于非参数等级的相关系数估计器，包括Spearman的Rho和Kendall's Tau。我们证明，非政治怀疑者可以达到图形恢复和参数估计的最佳收敛速率。该结果表明，即使数据确实是高斯，也可以将非承担图形模型用作安全替代流行的高斯图形模型。除了理论分析外，我们还进行了彻底的数值模拟，以比较理想和嘈杂设置下不同估计量的图恢复性能。然后将所提出的方法应用于大规模的基因组数据集，以说明其经验实用性。 R包大量实现了所提出的方法，可在综合R档案网络上获得：http：//cran.r-project.org/。
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/.