Two-sample test of sparse stochastic block models

2023/04/03 by Qianyong Wu, Wu, Qianyong, Hu Jiang +1
Mathematics · Physics and Astronomy · #Applications (stat.AP) #Complex Network Analysis Techniques #FOS: Computer and information sciences #Graph theory and applications #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2304.00739

openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper discusses a statistical problem related to testing for differences between two sparse networks with community structures. The community-wise edge probability matrices have entries of order O(n^-1/log n), where n represents the size of the network. The authors propose a test statistic that combines a method proposed by Wu et al. \citeWuTwoSampleSBM2022 and a resampling process. They derive the asymptotic null distribution of the test statistic and provide a guarantee of asymptotic power against the alternative hypothesis. To evaluate the performance of the proposed test statistic, the authors conduct simulations and provide real data examples. The results indicate that the proposed test statistic performs well in practice.

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