Sufficient dimension reduction for Gaussian copula graphical models

Abstract

We propose a sufficient dimension reduction method for recovering Gaussian copula graphical model which is very simple and computationally-efficient in the ultrahigh-dimensional setting. The screening of the conditional dependence graph is obtained by thresholding the elements of the rank-based correlation matrix estimator. The proposed approach possesses the sure screening property: with probability tending to 1, the estimated edge set contains the true edge set. We illustrate the performance of the proposed method in a simulation study and on a gene expression data. The result shows thatin practice it performs competitively with more complex and computationally-demandingtechniques for graph estimation.