Information Limits for Detecting a Subhypergraph
This work addresses a theoretical problem in hypergraph analysis, providing foundational limits for researchers in network science and machine learning, but it is incremental as it extends existing graph-based results to hypergraphs.
The paper tackles the problem of detecting a subhypergraph within a uniform hypergraph by analyzing adjacency tensors, establishing sharp information-theoretic limits for both weak and exact recovery. It shows that these conditions differ fundamentally from those in hypothesis testing literature.
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.