Learning continuous-time point processes is essential to many discrete event forecasting tasks. However, integration poses a major challenge, particularly for spatiotemporal point processes (STPPs), as it involves calculating the likelihood through triple integrals over space and time. Existing methods for integrating STPP either assume a parametric form of the intensity function, which lacks flexibility; or approximating the intensity with Monte Carlo sampling, which introduces numerical errors. Recent work by Omi et al. [2019] proposes a dual network or AutoInt approach for efficient integration of flexible intensity function. However, the method only focuses on the 1D temporal point process. In this paper, we introduce a novel paradigm: AutoSTPP (Automatic Integration for Spatiotemporal Neural Point Processes) that extends the AutoInt approach to 3D STPP. We show that direct extension of the previous work overly constrains the intensity function, leading to poor performance. We prove consistency of AutoSTPP and validate it on synthetic data and benchmark real world datasets, showcasing its significant advantage in recovering complex intensity functions from irregular spatiotemporal events, particularly when the intensity is sharply localized.

翻译：学习连续时间点过程对于许多离散事件预测任务至关重要。然而，积分构成了主要挑战，特别是对于时空点过程（STPP），因为它涉及通过时空三重积分计算似然。现有的STPP积分方法要么假设强度函数具有参数形式，缺乏灵活性；要么通过蒙特卡洛采样近似强度，引入数值误差。Omi等人[2019]近期的工作提出了一种双网络或AutoInt方法，用于高效积分灵活强度函数。然而，该方法仅关注一维时间点过程。本文引入了一种新范式：AutoSTPP（面向时空神经点过程的自动积分），将AutoInt方法扩展到三维STPP。我们表明，对先前工作的直接扩展会过度约束强度函数，导致性能不佳。我们证明了AutoSTPP的一致性，并在合成数据和基准真实世界数据集上进行了验证，展示了其在从不规则时空事件中恢复复杂强度函数方面的显著优势，尤其是当强度函数尖锐局部化时。