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Information limits for detecting a subhypergraph

Authors: Mingao Yuan; Zuofeng Shang;

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.

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Average
Green
gold