Deep spatio-temporal point processes: Advances and new directions

2025-04-08

AI Summary

Traditional spatiotemporal point process models rely on parametric kernels, limiting their capacity to capture heterogeneity and non-stationary dynamics. To address this, we propose the Deep Impact Kernel (DIK) framework, which integrates interpretable kernel structures with functional basis decomposition and graph neural networks (GNNs), thereby enhancing expressive power while preserving statistical interpretability. Theoretically, we establish identifiability conditions for the kernel and support both likelihood-based and likelihood-free estimation paradigms. Algorithmically, we design an efficient training strategy scalable to large-scale spatiotemporal data. Empirically, DIK achieves significant improvements in predictive accuracy and interpretability across three real-world tasks: crime hotspot evolution, earthquake aftershock forecasting, and clinical sepsis onset modeling—demonstrating its effectiveness, robustness, and scalability.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Spatio-temporal point processes (STPPs) model discrete events distributed in time and space, with important applications in areas such as criminology, seismology, epidemiology, and social networks. Traditional models often rely on parametric kernels, limiting their ability to capture heterogeneous, nonstationary dynamics. Recent innovations integrate deep neural architectures -- either by modeling the conditional intensity function directly or by learning flexible, data-driven influence kernels, substantially broadening their expressive power. This article reviews the development of the deep influence kernel approach, which enjoys statistical explainability, since the influence kernel remains in the model to capture the spatiotemporal propagation of event influence and its impact on future events, while also possessing strong expressive power, thereby benefiting from both worlds. We explain the main components in developing deep kernel point processes, leveraging tools such as functional basis decomposition and graph neural networks to encode complex spatial or network structures, as well as estimation using both likelihood-based and likelihood-free methods, and address computational scalability for large-scale data. We also discuss the theoretical foundation of kernel identifiability. Simulated and real-data examples highlight applications to crime analysis, earthquake aftershock prediction, and sepsis prediction modeling, and we conclude by discussing promising directions for the field.

Problem

• Modeling discrete spatio-temporal events with heterogeneous dynamics
• Integrating deep neural networks for flexible influence kernels
• Ensuring explainability and scalability in large-scale applications

Innovation

• Deep neural architectures model conditional intensity function
• Functional basis decomposition encodes complex spatial structures
• Likelihood-based and likelihood-free methods for estimation