High Dimensional Semiparametric Gaussian Copula Graphical Models

TL;DR

This paper introduces a robust semiparametric method for estimating high-dimensional Gaussian copula graphical models using rank-based correlations, achieving optimal convergence and demonstrating practical effectiveness in simulations and genomic data analysis.

Contribution

It proposes the nonparanormal skeptic, a novel approach that combines Gaussian copula models with rank-based estimators for robust high-dimensional graph estimation.

Findings

Achieves optimal parametric convergence rates in high dimensions.

Performs well in both ideal and noisy simulation settings.

Successfully applied to large-scale genomic data.

Abstract

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/.