Higher-Order Accurate Two-Sample Network Inference and Network Hashing

Meijia Shao

doi:10.1080/01621459.2025.2520459

Higher-Order Accurate Two-Sample Network Inference and Network Hashing

2025-08-05

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DOI：10.1080/01621459.2025.2520459

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Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural assumptions; achieving finite-sample higher-order accuracy; handling different network sizes and sparsity levels; fast computation and memory parsimony; controlling false discovery rate (FDR) in multiple testing; and theoretical understandings, particularly regarding finite-sample accuracy and minimax optimality. In this article, we develop a comprehensive toolbox, featuring a novel main method and its variants, all accompanied by strong theoretical guarantees, to address these challenges. Our method outperforms existing tools in speed and accuracy, and it is proved power-optimal. Our algorithms are user-friendly and versatile in handling various data structures (single or repeated network observations; known or unknown node registration). We also develop an innovative framework for offline hashing and fast querying as a very useful tool for large network databases. We showcase the effectiveness of our method through comprehensive simulations and applications to two real-world datasets, which revealed intriguing new structures. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Keywords:

Degeneracy

False-discovery rate

Higher-order accuracy

Nonparametric statistics

Network analysis

Higher-Order Accurate Two-Sample Network Inference and Network Hashing

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