A0579
Title: Statistical limits for testing the correlation of hypergraphs
Authors: Mingao Yuan - North Dakota State University (United States) [presenting]
Zuofeng Shang - New Jersey Institute of Technology (United States)
Abstract: The focus is on the hypothesis testing of correlation between two -uniform hypergraphs on unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperedges have the same marginal distributions as in the null hypothesis but are correlated after some unknown node permutation. We consider two scenarios: the hypergraphs are generated from the Gaussian-Wigner model and the dense Erd\"{o}s-R\'{e}nyi model. We derive the sharp information-theoretic testing threshold. Above the threshold, there exists a powerful test to distinguish the alternative hypothesis from the null hypothesis. Below the threshold, the alternative hypothesis and the null hypothesis are not distinguishable. The threshold involves and decreases as gets larger. This indicates testing the correlation of hypergraphs becomes easier than testing the correlation of graphs.