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arXiv · 2208.06503

Hypergraph reconstruction from noisy pairwise observations

Ariane Lizotte·Jean-Gabriel Young·Antoine Allard
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Abstract

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve precisely two entities-the pairwise case. Here we investigate the general problem of reconstructing a network in which higher-order interactions are also present. We study a minimal example of this problem, focusing on the case of hypergraphs with interactions between pairs and triplets of vertices, measured imperfectly and indirectly. We derive a Metropolis-Hastings-within-Gibbs algorithm for this model and use the algorithms to highlight the unique challenges that come with estimating higher-order models. We show that this approach tends to reconstruct empirical and synthetic networks more accurately than an equivalent graph model without higher-order interactions.

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Ariane Lizotte, Jean-Gabriel Young, Antoine Allard. 2022-08-12. Hypergraph reconstruction from noisy pairwise observations. https://doi.org/10.1038/s41598-023-48081-w

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