Using Maximum Entry-Wise Deviation to Test the Goodness of Fit for Stochastic Block Models

• Activity Number: 368 - Recent Advances in Statistical Network Analysis with Applications
• Type: Invited
• Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Graphics
• Author(s): Emma Jingfei Zhang*
• Companies: University of Miami
• Keywords: Community detection; Goodness of fit test; Stochastic block model; Increasing number of communities

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 talk, 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 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.