Identifying differential networks through high-dimensional two-sample inference

In this article, we identify differential networks within the Gaussian graphical model framework by examining the equivalence of two precision matrices. It is challenging work when the dimension of the precision matrix increases with the sample size. Existing methods typically assume sparsity in the precision matrix structure, a condition often unmet in real data. To address this issue, we introduce a statistic based on debiased estimator of the high-dimensional precision matrix and employ multiplier bootstrap to approximate the null distribution of the proposed statistic. The proposed method can be easily coupled with various estimation algorithms for high-dimensional precision matrix. In comparison with existing methods, the superiority of the proposed approach lies in mild structure constraints to the unknown precision matrix, making it robust to intricate conditional dependence structures in real data. Additionally, we introduce a cross-fitting procedure that utilizes full data information, leading to enhanced statistical power. Theoretical justification is provided to ensure the validity of the proposed method without restrictive assumptions. We showcase the effectiveness of our proposed method by simulation and real data example, which provides evidence of the proposed method’s usefulness and potential for application in various domains.