Statistical Testing on Directed Graphs by Surrogate Data Generation

2026-05-30

AI Summary

Existing nonparametric statistical testing methods based on surrogate data are primarily designed for undirected graphs and are ill-suited for directed graph structures. This work extends such approaches to the directed graph setting for the first time by defining wide-sense stationary signals through the eigendecomposition of graph shift operators and constructing a surrogate signal generation framework that preserves the covariance structure. Evaluated on real-world data, the proposed method significantly outperforms conventional undirected-graph approaches and naive permutation strategies, offering enhanced statistical power while maintaining test validity and practical feasibility.

Abstract

In recent years, graph signal processing has emerged as a powerful framework at the intersection of signal processing and graph theory, providing tools for the analysis of signals defined on nodes while accounting for their relationships represented by edges. These tools have been successfully applied to various settings, including statistical hypothesis testing. In particular, non-parametric approaches based on surrogate generation have been proposed for signals on undirected graphs. However, they are yet to be extended to directed graphs. In this work, we first revisit the notion of stationary graph signals on directed graphs. Specifically, and through the eigendecomposition of the graph shift operator, we define directed graph wide-sense stationary signals. Then, we propose a new framework to generate surrogate graph signals that preserve covariance structure under stationarity assumptions. Null distributions of the test metric can then be constructed from these surrogates and serve as a reference for the empirical data. Finally, we provide guiding examples and an application on real data, in which we compare the performance of our framework with existing techniques for undirected graphs or based on naive permutation, demonstrating feasibility and superiority of the proposed approach.

Problem

• directed graphs
• graph signal processing
• statistical hypothesis testing
• surrogate data generation
• stationary graph signals

Innovation

• directed graphs
• graph signal processing
• surrogate data
• stationarity
• statistical hypothesis testing