Kronecker-Structured Nonparametric Spatiotemporal Point Processes

2026-03-24

AI Summary

This work proposes a nonparametric spatiotemporal point process model based on Gaussian processes to overcome the limitations of traditional approaches, which often rely on restrictive parametric assumptions or lack interpretability in capturing complex event dependencies. The model employs a separable kernel and a structured grid to separately represent the background intensity and the triggering influence kernel, thereby achieving both flexibility and interpretability. To enhance scalability, the method leverages a Kronecker-structured covariance matrix and tensor-product Gauss–Legendre quadrature, enabling efficient handling of large-scale spatiotemporal event data. Experimental results demonstrate that the proposed approach significantly outperforms existing models across multiple real-world datasets, offering superior predictive accuracy and computational efficiency.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

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 graphs
• 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
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Events in spatiotemporal domains arise in numerous real-world applications, where uncovering event relationships and enabling accurate prediction are central challenges. Classical Poisson and Hawkes processes rely on restrictive parametric assumptions that limit their ability to capture complex interaction patterns, while recent neural point process models increase representational capacity but integrate event information in a black-box manner, hindering interpretable relationship discovery. To address these limitations, we propose a Kronecker-Structured Nonparametric Spatiotemporal Point Process (KSTPP) that enables transparent event-wise relationship discovery while retaining high modeling flexibility. We model the background intensity with a spatial Gaussian process (GP) and the influence kernel as a spatiotemporal GP, allowing rich interaction patterns including excitation, inhibition, neutrality, and time-varying effects. To enable scalable training and prediction, we adopt separable product kernels and represent the GPs on structured grids, inducing Kronecker-structured covariance matrices. Exploiting Kronecker algebra substantially reduces computational cost and allows the model to scale to large event collections. In addition, we develop a tensor-product Gauss-Legendre quadrature scheme to efficiently evaluate intractable likelihood integrals. Extensive experiments demonstrate the effectiveness of our framework.

Problem

• spatiotemporal point processes
• event relationships
• nonparametric modeling
• interpretability
• complex interaction patterns

Innovation

• Kronecker structure
• nonparametric point process
• spatiotemporal Gaussian process
• scalable inference
• tensor-product quadrature