Bayesian hypergraph inference from scarce and noisy dynamical observations

TL;DR

This paper introduces Bayes-THIS, a Bayesian hypergraph inference method that improves robustness and uncertainty quantification in reconstructing higher-order interactions from scarce, noisy dynamical data.

Contribution

It develops a Bayesian extension of Taylor-based hypergraph inference, incorporating automatic relevance determination for better performance in challenging data regimes.

Findings

Bayes-THIS outperforms fixed-threshold methods in noisy, limited data scenarios.

The Gaussian posterior enables uncertainty quantification and model validation.

Identifies a fundamental limitation where higher-order interactions are confounded with lower-order edges.

Abstract

Inferring higher-order interaction structure from observations of dynamics is a central challenge in complex systems, particularly when data are scarce, noisy, or concentrated in lower-dimensional regions of state space. We develop Bayes-THIS, a Bayesian extension of Taylor-based Hypergraph Inference using SINDy (THIS), which reconstructs hypergraph structure from time-series data by identifying sparse Taylor coefficients associated with pairwise and higher-order interactions. By replacing fixed-threshold sparse regression with sparse Bayesian regression using automatic relevance determination, Bayes-THIS explicitly models residual variance and applies adaptive, term-wise coefficient shrinkage, improving robustness in data-limited, high-noise, and ill-conditioned regimes. The resulting Gaussian posterior also enables an uncertainty-aware inference workflow: a posterior predictive check assesses whether the data contain sufficient higher-order signal to reliably support inference beyond a pairwise model, and credible-interval pruning selects hyperedges whose inferred coefficients are statistically distinguishable from zero. Finally, we characterize a fundamental limitation of the Taylor-based inference framework: when higher-order interactions concentrate on nodes that lack lower-order connections, the Taylor expansion systematically inflates lower-order coefficient estimates, producing spurious edges indistinguishable from genuine lower-order interactions. This structural non-identifiability cannot be resolved by either THIS or Bayes-THIS.