Kronecker-Structured Nonparametric Spatiotemporal Point Processes

TL;DR

This paper introduces KSTPP, a flexible and interpretable nonparametric spatiotemporal point process model that captures complex event interactions and scales efficiently to large datasets using Kronecker algebra.

Contribution

We propose a novel Kronecker-structured nonparametric model for spatiotemporal point processes that enhances interpretability and scalability over existing methods.

Findings

Effective modeling of complex interaction patterns including excitation and inhibition.

Scalable training and prediction enabled by Kronecker algebra and structured grids.

Demonstrated superior performance on large real-world datasets.

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.