A1313
Title: Two-sample test for stochastic block models via maximum entry-wise deviation
Authors: Kang Fu - Central China Normal University (China) [presenting]
Jianwei Hu - Central China Normal University (China)
Abstract: 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. Based on the maximum entry-wise deviation of the two centred and rescaled adjacency matrices, a novel test statistic is proposed to test two samples of stochastic block models. The null distribution of the proposed test statistic is proved to converge in distribution to a Gumbel distribution, and the change of the two samples from stochastic block models can be tested via the proposed method. Then, it is shown 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, the proposed method is also extended to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.
