A0462
Title: Using maximum entry-wise deviation to test the goodness-of-fit for stochastic block models
Authors: Emma Jingfei Zhang - Emory University (United States) [presenting]
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 interest in recent years. We propose a novel goodness-of-fit test based on the maximum entry of the centered and re-scaled 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 an 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.
