用时空神经霍克斯过程建模多变量事件，捕捉复杂交互模式。
Multivariate Spatio-Temporal Neural Hawkes Processes
- 通过学习时空衰减机制融合空间信息，灵活建模激发与抑制。
- 仿真中成功恢复多变量时空点模式的强度结构，传统方法失败。
- 适用于恐怖事件等多类型事件的时空关联分析，效果显著。
我们提出一种多变量时空神经霍克斯过程，用于建模具有时空动态的复杂多变量事件数据。该模型通过学习的时间与空间衰减机制，将空间信息融入潜在状态演化，扩展了连续时间神经霍克斯过程，无需预设触发核即可灵活建模激发与抑制。通过对基于深度学习的时序霍克斯模型拟合强度函数的分析，发现现有方法在捕捉强度行为方面存在建模空白，由此启发了本研究的时空方法。模拟研究表明，所提方法能有效恢复多变量时空点模式中的合理时空强度结构，而现有的时序神经霍克斯过程则无法做到。对巴基斯坦恐怖主义数据的应用进一步验证了该模型在捕捉多种事件类型间复杂时空交互方面的有效性。
原文摘要 · Abstract (English)
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.
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