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Using Maximum Entry-Wise Deviation to Test the Goodness of Fit for Stochastic Block Models
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2020-09-08 , DOI: 10.1080/01621459.2020.1722676
Jianwei Hu 1 , Jingfei Zhang 2 , Hong Qin 1, 3 , Ting Yan 1 , Ji Zhu 4
Affiliation  

Abstract–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. Supplementary materials for this article are available online.



中文翻译:

使用最大条目偏差测试随机块模型的拟合优度

摘要-随机块模型广泛用于检测网络数据中的社区结构。如何检验模型的拟合优度是基本问题之一,近年来受到越来越多的关注。在本文中,我们提出了一种新颖的拟合优度测试,该测试基于随机块模型的居中和重新缩放的邻接矩阵的最大条目。所提出的测试的一个显着优点是可以允许社区数量随着节点数量线性增长而忽略对数因子。我们证明了测试统计量的零分布在分布上收敛于 Gumbel 分布,并且我们表明社区的数量和成员向量都可以通过所提出的方法进行测试。此外,我们表明,所提出的测试具有针对一类替代方案的渐近功效保证。我们还证明了所提出的方法可以扩展到度校正随机块模型。模拟研究和真实世界的数据示例都表明所提出的方法运行良好。本文的补充材料可在线获取。

更新日期:2020-09-08
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