Leave-one-out testing for node-level differences in Gaussian graphical models

TL;DR

This paper introduces a leave-one-out Bartlett-adjusted test for node-level inference in Gaussian graphical models, improving localization and stability over classical methods, with validated simulations and practical case study.

Contribution

It proposes a novel node-level testing method using leave-one-out adjustments, enhancing localization and finite-sample stability in Gaussian graphical models.

Findings

Validates the test through simulations.

Demonstrates practical utility in a case study.

Achieves calibrated significance for individual nodes.

Abstract

We study two-sample equality testing in Gaussian graphical models. Classical likelihood ratio tests on decomposable graphs admit clique-wise factorizations, offering limited localization and unstable finite-sample behaviour. We propose node-level inference via a leave-one-out Bartlett-adjusted test on a fully connected graph. The resulting increments have standard chi-square null limits, enabling calibrated significance for single nodes and fixed-size subsets. Simulations confirm validity, and a case study shows practical utility.