Message-passing on hypergraphs: detectability, phase transitions and higher-order information
Open access
Date
2024-04Type
- Journal Article
ETH Bibliography
yes
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Abstract
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits. Here, we derive closed-form bounds for community detection in hypergraphs. Using a message-passing formulation, we demonstrate that detectability depends on the hypergraphs' structural properties, such as the distribution of hyperedge sizes or their assortativity. Our formulation enables a characterization of the entropy of a hypergraph in relation to that of its clique expansion, showing that community detection is enhanced when hyperedges highly overlap on pairs of nodes. We develop an efficient message-passing algorithm to learn communities and model parameters on large systems. Additionally, we devise an exact sampling routine to generate synthetic data from our probabilistic model. Using these methods, we numerically investigate the boundaries of community detection in synthetic datasets, and extract communities from real systems. Our results extend our understanding of the limits of community detection in hypergraphs and introduce flexible mathematical tools to study systems with higher-order interactions. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000670511Publication status
publishedExternal links
Journal / series
Journal of Statistical Mechanics: Theory and ExperimentVolume
Pages / Article No.
Publisher
IOP PublishingSubject
inference of graphical models; message-passing algorithms; statistical inferenceMore
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ETH Bibliography
yes
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