Statistical Limits for Testing Correlation of Random Hypergraphs

Document Type

Article

Publication Date

1-1-2024

Abstract

In this paper, we consider the hypothesis testing of correlation between two m-uniform hypergraphs on n unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperdges have the same marginal distributions as in the null hypothesis but are correlated after some unknown node permutation. We focus on two scenarios: the hypergraphs are generated from the Gaussian-Wigner model and the dense Erdös-Rényi 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 m and decreases as m gets larger. This indicates testing correlation of hypergraphs (m > 3) becomes easier than testing correlation of graphs (m = 2).

Identifier

85191890878 (Scopus)

Publication Title

Alea (Rio de Janeiro)

External Full Text Location

https://doi.org/10.30757/ALEA.v21-19

ISSN

19800436

First Page

465

Last Page

489

Volume

21

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