Autoregressive Hypergraph

2025-06-20

AI Summary

Real-world multi-entity interactions—such as collaborative projects or protein complexes—naturally form non-uniform hypergraphs, yet existing models neglect their temporal dynamics. This paper introduces the first theoretically grounded first-order autoregressive (AR(1)) framework to characterize edge persistence and evolutionary mechanisms in dynamic non-uniform hypergraphs. Methodologically, we integrate the hypergraph Laplacian, spectral clustering, maximum likelihood estimation, and likelihood-ratio-based change-point detection to construct the first interpretable dynamic hypergraph model for multi-entity interactions. Theoretical contributions include closed-form probabilistic characterizations, uniform error bounds, and asymptotic normality; we further propose the first spectral clustering and change-point detection algorithms tailored to the hypergraph stochastic block model. Extensive experiments on synthetic data, primary-school interaction records, and the Enron email corpus demonstrate accurate identification of temporal community structure and structural breakpoints.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Modeling multi-entity interactions in dynamic hypergraphs
• Addressing temporal evolution in relational hypergraph data
• Detecting structural breaks in hypergraph time series

Innovation

• First-order autoregressive model for dynamic hypergraphs
• Novel Laplacian enables efficient community recovery
• Likelihood-based estimator detects structural breaks