Optimal Network Pairwise Comparison

• 成果类型: Article
• 署名作者: Jin, Jiashun; Ke, Zheng Tracy; Luo, Shengming; Ma, Yucong
• 署名单位: Carnegie Mellon University; Harvard University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2393471
• 发表日期: 2025
• 页码: 1048-1062
• 关键词: hypothesis-testing problem; community detection; matrices

摘要

We are interested in the problem of two-sample network hypothesis testing: given two networks with the same set of nodes, we wish to test whether the underlying Bernoulli probability matrices of the two networks are the same or not. We propose Interlacing Balance Measure (IBM) as a new two-sample testing approach. We consider the Degree-Corrected Mixed-Membership (DCMM) model for undirected networks, where we allow severe degree heterogeneity, mixed-memberships, flexible sparsity levels, and weak signals. In such a broad setting, how to find a test that has a tractable limiting null and optimal testing performances is a challenging problem. We show that IBM is such a test: in a broad DCMM setting with only mild regularity conditions, IBM has N(0,1) as the limiting null and achieves the optimal phase transition. While the above is for undirected networks, IBM is a unified approach and is directly implementable for directed networks. For a broad directed-DCMM (extension of DCMM for directed networks) setting, we show that IBM has N(0,1/2) as the limiting null and continues to achieve the optimal phase transition. We have also applied IBM to the Enron email network and a gene co-expression network, with interesting results. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.