Automatic Integration for Spatiotemporal Neural Point Processes

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.