Hypergraph reconstruction from noisy pairwise observations

TL;DR

This paper addresses the challenge of reconstructing hypergraphs with higher-order interactions from noisy, indirect measurements, proposing a novel algorithm that improves accuracy over traditional pairwise models.

Contribution

It introduces a Metropolis-Hastings-within-Gibbs algorithm for hypergraph reconstruction from noisy data, highlighting the benefits of modeling higher-order interactions.

Findings

The proposed method outperforms pairwise models in accuracy.

Higher-order interaction modeling captures complex network structures.

The algorithm effectively handles noisy, indirect measurements.

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.