Stochastic block model is a popular tool for detecting community structures in network data. How to detect the difference of the community structures is an important issue for stochastic block models. However, two--sample test has been a largely under explored domain, and too little work has been devoted to it. In this article, based on maximum entry--wise deviation of the two centered and rescaled adjacency matrices, we propose a novel test statistic to test two samples of stochastic block models. We prove that the null distribution of the proposed test statistic converges in distribution to a Gumbel distribution, and we show the change of the two samples for stochastic block models can be tested via the proposed method. Further, we show that the proposed test has asymptotic power guarantee against alternative models. One noticeable advantage of the proposed test statistic is that the number of communities can be allowed to grow linearly up to a logarithmic factor. Both simulation studies and real-world data examples indicate that the proposed method works well.
翻译:在网络数据中检测社区结构的流行工具中,stocketic 区块模型是发现社区结构差异的流行工具。 如何检测社区结构差异是随机区块模型的一个重要问题。 但是,两样样的测试在很大程度上是在探索的领域之下进行,而且只做了很少的工作。 在本条中,基于两个中央和重新测量的相邻矩阵的最大切入偏差,我们提出了一个新颖的测试统计,以测试两个随机区块模型的样本。我们证明,拟议的测试统计数据的无效分布在分布到 Gumbel 分布中,我们展示了两种随机区块模型样本的变化可以通过拟议方法进行测试。此外,我们证明,拟议的测试对替代模型具有无药力保证。提议的测试统计的一个显著优点是,允许社区数量直线增长到对数系数。模拟研究和真实世界数据实例都表明,拟议方法效果良好。