
arXiv: 2105.02259
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.
FOS: Computer and information sciences, sharp information-theoretic condition, uniform hypergraph, Computer Science - Information Theory, Information Theory (cs.IT), Statistics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), exact recovery, Statistics - Machine Learning, weak recovery, FOS: Mathematics
FOS: Computer and information sciences, sharp information-theoretic condition, uniform hypergraph, Computer Science - Information Theory, Information Theory (cs.IT), Statistics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), exact recovery, Statistics - Machine Learning, weak recovery, FOS: Mathematics
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