Information Limits for Detecting a Subhypergraph

TL;DR

This paper investigates the fundamental information-theoretic limits for detecting and recovering a subhypergraph within a uniform hypergraph, providing sharp conditions for both weak and exact recovery.

Contribution

It establishes novel, sharp information-theoretic bounds for subhypergraph detection and recovery, highlighting differences from traditional hypothesis testing results.

Findings

Derived sharp conditions for weak recovery

Derived sharp conditions for exact recovery

Revealed fundamental differences from hypothesis testing literature

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.