Gauss关联结构图模型的充分降维方法

Sufficient dimension reduction for Gaussian copula graphical models

本文提出了恢复Gauss关联结构(copula)图模型的充分降维方法,该方法在超高维情形下具有很高的计算效率.本质上,充分降维是通过对利用非参数方法估计的相关系数矩阵进行截断来实现的.本文给出了所提方法的理论性质,保证其所估计的边集合以概率趋于1覆盖所有真实存在边的集合.数值模拟研究发现,本文所提方法与现存方法相比有相近的估计表现,而计算效率却更高.最后分析了一组基因数据来展示本文所提方法的实际应用表现.

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 that in practice it performs competitively with more complex and computationally-demanding techniques for graph estimation.