arXiv:2603.23746cs.LG2026-03

提出可解释的时空点过程模型,精准捕捉事件间复杂关系。

Kronecker-Structured Nonparametric Spatiotemporal Point Processes

  • 用克罗内克结构建模时空交互,提升可解释性与灵活性
  • 支持激发、抑制等多样互动模式,时间动态效应可建模
  • 计算高效,适合大规模事件数据,适合需要透明建模的研究者

时空域中的事件在众多现实应用中广泛存在,揭示事件间关系并实现准确预测是核心挑战。传统泊松和霍克斯过程依赖严格参数假设,难以捕捉复杂交互模式;近期神经点过程虽增强表达能力,但以黑箱方式整合事件信息,不利于关系可解释发现。为此,我们提出克罗内克结构非参数时空点过程(KSTPP),在保持高建模灵活性的同时,实现事件级关系的透明发现。背景强度采用空间高斯过程(GP)建模,影响核函数则为时空高斯过程,能刻画激发、抑制、中性及随时间变化的效应。为实现可扩展训练与预测,采用可分离乘积核并在结构化网格上表示高斯过程,诱导出克罗内克结构协方差矩阵,显著降低计算成本,使模型可扩展至大规模事件集合。此外,设计张量积高斯-勒让德求积方案,高效处理不可解析的似然积分。大量实验验证了该框架的有效性。

原文摘要 · Abstract (English)

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.

点过程时空建模可解释性高斯过程

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。