Autoregressive Hypergraph

TL;DR

This paper introduces a novel autoregressive hypergraph model for dynamic, non-uniform hypergraphs, providing theoretical guarantees, efficient inference, community detection, and change-point estimation, with demonstrated effectiveness on real-world datasets.

Contribution

It presents the first dynamic hypergraph model with provable guarantees, including a spectral clustering method for community detection and a change-point estimator, advancing the analysis of evolving complex relational data.

Findings

Effective community detection via spectral clustering.

Accurate change-point detection in hypergraph time series.

Validated methods on real-world datasets with meaningful insights.

Abstract

Traditional graph representations are insufficient for modelling real-world phenomena involving multi-entity interactions, such as collaborative projects or protein complexes, necessitating the use of hypergraphs. While hypergraphs preserve the intrinsic nature of such complex relationships, existing models often overlook temporal evolution in relational data. To address this, we introduce a first-order autoregressive (i.e. AR(1)) model for dynamic non-uniform hypergraphs. This is the first dynamic hypergraph model with provable theoretical guarantees, explicitly defining the temporal evolution of hyperedge presence through transition probabilities that govern persistence and change dynamics. This framework provides closed-form expressions for key probabilistic properties and facilitates straightforward maximum-likelihood inference with uniform error bounds and asymptotic normality, along with a permutation-based diagnostic test. We also consider an AR(1) hypergraph stochastic block model (HSBM), where a novel Laplacian enables exact and efficient latent community recovery via a spectral clustering algorithm. Furthermore, we develop a likelihood-based change-point estimator for the HSBM to detect structural breaks within the time series. The efficacy and practical value of our methods are comprehensively demonstrated through extensive simulation studies and compelling applications to a primary school interaction data set and the Enron email corpus, revealing insightful community structures and significant temporal changes.