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.

中文翻译：

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检测超图的信息限制

我们考虑基于对应于统一超图的观测到的邻接张量来恢复超图的问题。假设统一超图包含称为子超图的顶点子集。假设限制在超图上的边与其他边相比遵循不同的概率分布。我们考虑亚超图的弱恢复和精确恢复，并在每种情况下建立信息理论极限。具体来说，我们为从信息理论的角度弱或准确恢复亚超级图建立了清晰的条件。这些条件与假设检验文献中得出的条件基本不同。