Academic

Kronecker-Structured Nonparametric Spatiotemporal Point Processes

arXiv:2603.23746v1 Announce Type: new 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

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Zhitong Xu, Qiwei Yuan, Yinghao Chen, Yan Sun, Bin Shen, Shandian Zhe · · 1 min read · 2 views
#cs.LG

arXiv:2603.23746v1 Announce Type: new 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.

Executive Summary

This article introduces the Kronecker-Structured Nonparametric Spatiotemporal Point Process (KSTPP), a novel framework designed to address the limitations of classical Poisson and Hawkes processes, as well as recent neural point process models. By leveraging spatial and spatiotemporal Gaussian processes, the KSTPP enables transparent event-wise relationship discovery while retaining high modeling flexibility. Key innovations include separable product kernels, structured grid representations, and a tensor-product Gauss-Legendre quadrature scheme. The proposed model demonstrates the ability to capture complex interaction patterns, including excitation, inhibition, neutrality, and time-varying effects. Extensive experiments showcase the effectiveness of the KSTPP, offering a promising solution for spatiotemporal event modeling. This development has significant implications for various applications, including but not limited to, natural hazard prediction, epidemiology, and smart cities.

Key Points

  • ▸ The KSTPP combines the strengths of Gaussian processes and point processes to capture complex event relationships.
  • ▸ The model incorporates separable product kernels and structured grid representations to enable scalable training and prediction.
  • ▸ The tensor-product Gauss-Legendre quadrature scheme efficiently evaluates intractable likelihood integrals.

Merits

Strength in modeling flexibility

The KSTPP retains high modeling flexibility, enabling it to capture a wide range of event relationships and interaction patterns.

Transparency in relationship discovery

The model provides transparent event-wise relationship discovery, allowing for interpretable insights into event interactions.

Demerits

Computational complexity

The KSTPP's computational cost is reduced by exploiting Kronecker algebra, but may still be significant for very large event collections.

Expert Commentary

The KSTPP is a significant contribution to the field of spatiotemporal event modeling, addressing the limitations of existing approaches through a novel combination of Gaussian processes and point processes. While the model's computational complexity is a consideration, the proposed framework offers a promising solution for capturing complex event relationships and interaction patterns. As the field continues to evolve, it will be essential to further explore the applications and limitations of the KSTPP, as well as its potential intersections with other areas of research.

Recommendations

  • ✓ Further investigation into the KSTPP's performance on large-scale event collections and its potential applications in real-world scenarios.
  • ✓ Exploration of the model's intersections with other areas of research, such as neural point process models and Gaussian process-based models.

Sources

Original: arXiv - cs.LG

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