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 approach for efficient integration of flexible intensity function. However, their 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 dual network approach to 3D STPP. While previous work provides a foundation, its direct extension overly restricts the intensity function and leads to computational challenges. In response, we introduce a decomposable parametrization for the integral network using ProdNet. This approach, leveraging the product of simplified univariate graphs, effectively sidesteps the computational complexities inherent in multivariate computational graphs. We prove the consistency of AutoSTPP and validate it on synthetic data and benchmark real-world datasets. AutoSTPP shows a significant advantage in recovering complex intensity functions from irregular spatiotemporal events, particularly when the intensity is sharply localized. Our code is open-source at https://github.com/Rose-STL-Lab/AutoSTPP.

翻译：学习连续时间点过程对许多离散事件预测任务至关重要。然而，积分构成了一项重大挑战，特别是在时空点过程中，因为需要通过空间和时间的三重积分来计算似然函数。现有的时空点过程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]近期提出了一种双网络方法，用于高效积分灵活强度函数，但其方法仅关注一维时间点过程。本文提出了一种新范式：AutoSTPP（自动积分时空神经点过程），将双网络方法扩展至三维时空点过程。虽然先前工作提供了基础，但直接扩展会过度限制强度函数，并引发计算挑战。为此，我们引入基于ProdNet的可分解参数化积分网络，该方法利用简化单变量图的乘积，有效规避了多变量计算图固有的计算复杂性。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。AutoSTPP在从不规则时空事件中恢复复杂强度函数方面展现出显著优势，尤其当强度函数呈现尖锐局部化特征时。我们的代码已开源：https://github.com/Rose-STL-Lab/AutoSTPP。