Higher-order accurate two-sample network inference and network hashing

TL;DR

This paper introduces a comprehensive, theoretically-guaranteed toolbox for two-sample network inference that improves accuracy, speed, and versatility, and includes a novel network hashing framework for large datasets.

Contribution

It presents a new method with strong theoretical guarantees for network comparison, handling various data structures, and introduces a novel network hashing framework for large-scale analysis.

Findings

Outperforms existing tools in speed and accuracy

Proved to be power-optimal in hypothesis testing

Effectively reveals new network structures in real data

Abstract

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 paper, 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.