DeepAI

# Sharp detection boundaries on testing dense subhypergraph

We study the problem of testing the existence of a dense subhypergraph. The null hypothesis is an Erdos-Renyi uniform random hypergraph and the alternative hypothesis is 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 detectable 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.

• 12 publications
• 27 publications
04/08/2021

### Heterogeneous Dense Subhypergraph Detection

We study the problem of testing the existence of a heterogeneous dense s...
02/25/2019

### Configuration Models of Random Hypergraphs and their Applications

Networks of dyadic relationships between entities have emerged as a domi...
10/06/2021

### Sharp Signal Detection Under Ferromagnetic Ising Models

In this paper we study the effect of dependence on detecting a class of ...
08/13/2013

### Community Detection in Sparse Random Networks

We consider the problem of detecting a tight community in a sparse rando...
05/05/2021

### Information Limits for Detecting a Subhypergraph

We consider the problem of recovering a subhypergraph based on an observ...
08/24/2022

### An asymptotic resolution of a conjecture of Szemerédi and Petruska

Consider a 3-uniform hypergraph of order n with clique number k such tha...
10/04/2021

### Hypergraph regularity and random sampling

Suppose a k-uniform hypergraph H that satisfies a certain regularity ins...