DeepAI

# Information Limits for Detecting a Subhypergraph

We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges restricted to the subhypergraph are assumed to follow a different probability distribution than other edges. We consider both weak recovery and exact recovery of the subhypergraph, and establish information-theoretic limits in each case. Specifically, we establish sharp conditions for the possibility of weakly or exactly recovering the subhypergraph from an information-theoretic point of view. These conditions are fundamentally different from their counterparts derived in hypothesis testing literature.

• 12 publications
• 27 publications
11/16/2018

### Exact Recovery in the Hypergraph Stochastic Block Model: a Spectral Algorithm

We consider the exact recovery problem in the hypergraph stochastic bloc...
03/22/2022

### Spectral Algorithms Optimally Recover (Censored) Planted Dense Subgraphs

We study spectral algorithms for the planted dense subgraph problem (PDS...
11/23/2020

### Statistical and computational thresholds for the planted k-densest sub-hypergraph problem

Recovery a planted signal perturbed by noise is a fundamental problem in...
12/21/2017

### On Adjacency and e-adjacency in General Hypergraphs: Towards an e-adjacency Tensor

Adjacency between two vertices in graphs or hypergraphs is a pairwise re...
07/20/2021

### Limits of Detecting Extraterrestrial Civilizations

The search for extraterrestrial intelligence (SETI) is a scientific ende...
01/12/2021

### Sharp detection boundaries on testing dense subhypergraph

We study the problem of testing the existence of a dense subhypergraph. ...
02/21/2022

### On the Information-theoretic Security of Combinatorial All-or-nothing Transforms

All-or-nothing transforms (AONT) were proposed by Rivest as a message pr...