Hypergraph reconstruction from noisy pairwise observations

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.

References in corpus (5)

• Cooperative Game Theory Approaches for Network Partitioning
• The physics of higher-order interactions in complex systems
• Principles of scientific research team formation and evolution
• $\beta$ models for random hypergraphs with a given degree sequence
• Higher-Order Spectral Clustering under Superimposed Stochastic Block Model

Cited by in corpus (4)

• Collective dynamics on higher-order networks
• Mining higher-order triadic interactions
• Higher-order dissimilarity measures for hypergraph comparison
• Symmetry-driven embedding of networks in hyperbolic space