Information limits for detecting a subhypergraph

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 the hypothesis testing literature.