High Dimensional Semiparametric Gaussian Copula Graphical Models
This provides a more flexible and robust method for statisticians and data scientists working with high-dimensional data, such as in genomics, though it builds incrementally on existing Gaussian copula models.
The paper tackles the problem of estimating high-dimensional undirected graphical models by proposing a semiparametric approach called nonparanormal skeptic, which achieves optimal parametric convergence rates in graph and parameter estimation, making it a robust alternative to Gaussian graphical models even with Gaussian data.
In this paper, 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 nonparanormal) 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 celebrating 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. The proposed methods are then applied on a large-scale genomic dataset to illustrate their empirical usefulness. The R language software package huge implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran. r-project.org/.