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Neural Spatiotemporal Point Processes: Trends and Challenges

Sumantrak Mukherjee, Mouad Elhamdi, George Mohler, David A. Selby, Yao Xie, Sebastian Vollmer, Gerrit Grossmann

TL;DR

The paper surveys neural spatiotemporal point processes (STPPs), framing STPPs via conditional intensity functions and likelihood-based inference to model events in continuous space and time. It organizes approaches around history encoding, single- and multi-event prediction, and spatial encoding through kernels, context, and continuous-time formulations, including diffusion-based generative methods and score-matching techniques. Key contributions include a unified view of kernel families (stationary and non-stationary), context integration, and continuous-time neural methods, plus a discussion of training/inference strategies (automatic integration, amortized VI, and RL imitation) and thorough evaluation metrics. The survey also highlights open challenges—reproducibility, benchmarks, architectures, applicability, and causality/uncertainty—that shape future research and practical deployment in domains such as disaster response, urban crime, traffic, and epidemiology.

Abstract

Spatiotemporal point processes (STPPs) are probabilistic models for events occurring in continuous space and time. Real-world event data often exhibit intricate dependencies and heterogeneous dynamics. By incorporating modern deep learning techniques, STPPs can model these complexities more effectively than traditional approaches. Consequently, the fusion of neural methods with STPPs has become an active and rapidly evolving research area. In this review, we categorize existing approaches, unify key design choices, and explain the challenges of working with this data modality. We further highlight emerging trends and diverse application domains. Finally, we identify open challenges and gaps in the literature.

Neural Spatiotemporal Point Processes: Trends and Challenges

TL;DR

The paper surveys neural spatiotemporal point processes (STPPs), framing STPPs via conditional intensity functions and likelihood-based inference to model events in continuous space and time. It organizes approaches around history encoding, single- and multi-event prediction, and spatial encoding through kernels, context, and continuous-time formulations, including diffusion-based generative methods and score-matching techniques. Key contributions include a unified view of kernel families (stationary and non-stationary), context integration, and continuous-time neural methods, plus a discussion of training/inference strategies (automatic integration, amortized VI, and RL imitation) and thorough evaluation metrics. The survey also highlights open challenges—reproducibility, benchmarks, architectures, applicability, and causality/uncertainty—that shape future research and practical deployment in domains such as disaster response, urban crime, traffic, and epidemiology.

Abstract

Spatiotemporal point processes (STPPs) are probabilistic models for events occurring in continuous space and time. Real-world event data often exhibit intricate dependencies and heterogeneous dynamics. By incorporating modern deep learning techniques, STPPs can model these complexities more effectively than traditional approaches. Consequently, the fusion of neural methods with STPPs has become an active and rapidly evolving research area. In this review, we categorize existing approaches, unify key design choices, and explain the challenges of working with this data modality. We further highlight emerging trends and diverse application domains. Finally, we identify open challenges and gaps in the literature.

Paper Structure

This paper contains 31 sections, 8 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Why we need neural STPPs.
  3. Scope and structure of the paper.
  4. Background and Notation
  5. Spatiotemporal point processes.
  6. Likelihood.
  7. Intensity function.
  8. Modeling Neural Spatiotemporal Point Processes
  9. History Event Encoder
  10. Single Event Prediction
  11. Kernel-based methods.
  12. Non-stationary kernels.
  13. Context.
  14. Semi-parametric and non-parametric kernels.
  15. Continuous time-based methods.
  16. ...and 16 more sections

Figures (2)

  • Figure 1: Schematic of the autoregressive construction of an STPP with two spatial dimensions. Three events are fed into an NN that predicts the likelihood of future event times and locations.
  • Figure 2: A timeline of the reviewed methodological and application-focused works, along with an overview of neural architectures and application domains. Papers are grouped based on how they encode spatial information, though in some cases these categorizations are not strictly defined.