Sharp detection boundaries on testing dense subhypergraph

Document Type

Article

Publication Date

11-1-2022

Abstract

We study the problem of testing the existence of a dense subhypergraph. The null hypothesis corresponds to an Erdős-Rényi uniform random hypergraph and the alternative hypothesis corresponds to a uniform random hypergraph that contains a dense subhypergraph. We establish sharp detection boundaries in both scenarios: (1) the edge probabilities are known; (2) the edge probabilities are unknown. In both scenarios, sharp detection boundaries are characterized by the appropriate model parameters. Asymptotically powerful tests are provided when the model parameters fall in the detectable regions. Our results indicate that the detectable regions for general hypergraph models are dramatically different from their graph counterparts.

Identifier

85136296279 (Scopus)

Publication Title

Bernoulli

External Full Text Location

https://doi.org/10.3150/21-BEJ1425

ISSN

13507265

First Page

2459

Last Page

2491

Issue

4

Volume

28

Grant

1764280

Fund Ref

National Science Foundation

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