Deep Spatiotemporal Point Processes: Advances and New Directions

Spatiotemporal point processes model discrete events distributed in space and time, with applications in criminology, seismology, epidemiology, and social networks. Classical models rely on parametric kernels, limiting their ability to capture heterogeneous, nonstationary dynamics. Recent advances integrate deep neural architectures, either by modeling the conditional intensity directly or by learning flexible, data-driven influence kernels. This article reviews the deep influence kernel approach, which balances statistical interpretability by retaining explicit kernels to capture event propagation, with expressive power from neural architectures. We outline key components, including functional basis decomposition, graph neural networks for encoding spatial or network structures, and both likelihood-based and likelihood-free estimation methods, while addressing scalability for large data. We also highlight theoretical results on kernel identifiability. Applications in crime analysis, earthquake aftershock prediction, and sepsis modeling demonstrate the framework's effectiveness. We conclude with promising directions for developing explainable and scalable deep kernel point processes.