Using Maximum Entry-Wise Deviation to Test the Goodness of Fit for Stochastic Block Models

• 成果类型: Article
• 署名作者: Hu, Jianwei; Zhang, Jingfei; Qin, Hong; Yan, Ting; Zhu, Ji
• 署名单位: Central China Normal University; University of Miami; Zhongnan University of Economics & Law; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1722676
• 发表日期: 2021
• 页码: 1373-1382
• 关键词: Community Detection; blockmodels; Consistency; prediction

摘要

The stochastic block model is widely used for detecting community structures in network data. How to test the goodness of fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article, we propose a novel goodness-of-fit test based on the maximum entry of the centered and rescaled adjacency matrix for the stochastic block model. One noticeable advantage of the proposed test is that the number of communities can be allowed to grow linearly with the number of nodes ignoring a logarithmic factor. We prove that the null distribution of the test statistic converges in distribution to a Gumbel distribution, and we show that both the number of communities and the membership vector can be tested via the proposed method. Furthermore, we show that the proposed test has asymptotic power guarantee against a class of alternatives. We also demonstrate that the proposed method can be extended to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.for this article are available online.