Goodness-of-fit tests for high-dimensional Gaussian graphical models via exchangeable sampling
提出一种适用于低维和高维高斯图模型的拟合优度检验框架，通过可交换抽样算法实现精确有限样本误差控制，在精度矩阵存在许多小非零项时检验功效优于现有方法。
Abstract We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on sufficient statistics. This framework provides exact finite-sample error control regardless of the dimension and allows flexible choices of test statistics to improve power. We explore several candidate test statistics and conduct extensive simulation studies to demonstrate their finite-sample performance compared to existing methods. The proposed tests exhibit superior power, particularly in cases where the true precision matrix deviates from the null hypothesis due to many small nonzero entries. To justify theoretically, we consider a high-dimensional setting where the proposed test achieves rate-optimality under two distinct signal patterns in the precision matrix: (1) dense patterns with many small nonzero entries and (2) strong patterns with at least one large entry. Finally, we illustrate the usefulness of the proposed test through real-world applications.