Information Limits for Detecting a Subhypergraph
Information Theory
2021-05-07 v1 math.IT
Statistics Theory
Machine Learning
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2105.02259,
title = {Information Limits for Detecting a Subhypergraph},
author = {Mingao Yuan and Zuofeng Shang},
journal= {arXiv preprint arXiv:2105.02259},
year = {2021}
}