Flexible and Scalable Bayesian Modelling of Spatio-Temporal Hawkes Processes

2026-03-30

AI Summary

Existing spatiotemporal Hawkes process models often rely on parametric or semi-parametric assumptions, limiting their ability to flexibly capture complex dynamics between endogenous and exogenous events. This work proposes the first Bayesian nonparametric spatiotemporal Hawkes process model based on additive Gaussian processes, which decouples the spatiotemporal background intensity from the triggering kernel. This design enhances interpretability while preserving high flexibility and enabling principled uncertainty quantification. Leveraging sparse variational inference with a Gaussian variational family, the model achieves efficient and scalable learning. Experiments demonstrate that the method accurately recovers background and triggering structures on synthetic data, attains higher leave-one-out log-likelihood on real-world datasets, and reveals interpretable self-exciting spatiotemporal patterns.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Bayesian LearningCognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSemantics 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

Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian nonparametric framework for spatio-temporal Hawkes processes using additive Gaussian processes for the prior distributions on the background rate and the triggering kernel. This additive structure enhances interpretability by decoupling temporal and spatial effects while maintaining high modelling flexibility across the entire spatio-temporal domain. To address scalability, we develop a sparse variational inference scheme based on the Gaussian variational family. Synthetic experiments demonstrate that the proposed method accurately recovers background and triggering structures, achieving superior performance compared to existing alternatives. When applied to real-world datasets, it achieves higher held-out log-likelihoods and reveals interpretable spatio-temporal structures of the self-excitation mechanism. Overall, the framework provides a flexible, scalable, interpretable, and uncertainty-aware approach for modelling complex excitation patterns in spatio-temporal event data.

Problem

• spatio-temporal Hawkes processes
• nonparametric modeling
• background rate
• triggering kernel
• event dynamics

Innovation

• Bayesian nonparametrics
• spatio-temporal Hawkes processes
• additive Gaussian processes
• sparse variational inference
• self-excitation