We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial information into latent state evolution through learned temporal and spatial decay dynamics, enabling flexible modeling of excitation and inhibition without predefined triggering kernels. By analyzing fitted intensity functions of deep learning-based temporal Hawkes process models, we identify a modeling gap in how fitted intensity behavior is captured beyond likelihood-based performance, which motivates the proposed spatio-temporal approach. Simulation studies show that the proposed method successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns, while existing temporal neural Hawkes process approach fails to do so. An application to terrorism data from Pakistan further demonstrates the proposed model's ability to capture complex spatio-temporal interaction across multiple event types.

翻译：我们提出了一种多元时空神经霍克斯过程，用于建模具有时空动态的复杂多元事件数据。该模型通过将空间信息整合到潜在状态演化中，扩展了连续时间神经霍克斯过程，具体通过学习到的时间与空间衰减动态来实现，从而能够灵活地建模激励与抑制效应，而无需预定义触发核。通过分析基于深度学习的时间霍克斯过程模型的拟合强度函数，我们发现了一个建模空白：在基于似然的性能之外，如何捕捉拟合强度的行为特征，这促使我们提出这种时空建模方法。仿真研究表明，所提方法能成功恢复多元时空点模式中合理的时间与空间强度结构，而现有的时间神经霍克斯过程方法则无法做到。在巴基斯坦恐怖主义数据上的应用进一步证明了该模型能够捕捉跨多种事件类型的复杂时空交互作用。