论文标题
通过最大入口偏差的随机块模型的两样本测试
Two-Sample Test for Stochastic Block Models via Maximum Entry-wise Deviation
论文作者
论文摘要
随机块模型是检测网络数据中社区结构的流行工具。检测两个社区结构之间的差异是随机块模型的重要问题。但是，两样本测试在很大程度上是一个不足探索的域，而且工作太少了。在本文中，基于两个居中和重新缩放的邻接矩阵的最大输入偏差，我们提出了一种新型的测试统计量来测试两个随机块模型的样本。我们证明，所提出的测试统计量的零分布在分布中收敛到牙龈分布，我们显示了可以通过提出的方法测试从随机块模型中的两个样本的变化。然后，我们表明该提出的测试具有针对替代模型的渐近功率保证。所提出的测试统计数据的一个明显优势是，可以允许社区的数量线性发展到对数因素。此外，我们将提出的方法扩展到了经验校正的随机块模型。仿真研究和现实世界数据示例均表明该方法效果很好。
The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has been a largely under-explored domain, and too little work has been devoted to it. In this article, based on the 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 from stochastic block models can be tested via the proposed method. Then, we show that the proposed test has an 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. Further, we extend the proposed method to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.
