Statistics Department Seminar Series: Yang Feng, Associate Professor, Department of Statistics, Columbia University

A fundamental problem in network data analysis is to test whether a network contains statistically significant communities. We study this problem in the stochastic block model context by testing H0: Erdos-Renyi model vs. H1: stochastic block model. This problem serves as the foundation for many other problems including the testing-based methods for determining the number of communities and community detection. Results will be presented for both ordinary graphs as well as hypergraphs where each edge contains more than two vertices. A comprehensive study is conducted for a wide spectrum of edge (or hyperedge) density scenarios. In particular, the joint impact of signal-to-noise ratio and the number of communities on the asymptotic results is unveiled. The proposed testing procedures are examined by both simulated and real-world network datasets. The talk is based on joint work with Mingao Yuan, Ruiqi Liu, and Zuofeng Shang.