# A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications

arXiv: https://arxiv.org/abs/1708.02647 · HTML: https://mlsanity.com/paper/1708.02647/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2017.

## Built on by (most cited first, 30 of 40)

- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [Neural Point Process for Learning Spatiotemporal Event Dynamics](https://mlsanity.com/paper/2112.06351/) (2021)
- [The effect of differential victim crime reporting on predictive policing systems](https://mlsanity.com/paper/2102.00128/) (2021)
- [Automatic Integration for Spatiotemporal Neural Point Processes](https://mlsanity.com/paper/2310.06179/) (2023)
- [Mitigating Performance Saturation in Neural Marked Point Processes: Architectures and Loss Functions](https://mlsanity.com/paper/2107.03354/) (2021)
- [Neural Spectral Marked Point Processes](https://mlsanity.com/paper/2106.10773/) (2021)
- [TimeGraph: Synthetic Benchmark Datasets for Robust Time-Series Causal Discovery](https://mlsanity.com/paper/2506.01361/) (2025)
- [Spatio-temporal point processes with deep non-stationary kernels](https://mlsanity.com/paper/2211.11179/) (2022)
- [Sequential change-point detection for mutually exciting point processes over networks](https://mlsanity.com/paper/2102.05724/) (2021)
- [Conditional Generative Modeling for High-dimensional Marked Temporal Point Processes](https://mlsanity.com/paper/2305.12569/) (2023)
- [Intensity-free Convolutional Temporal Point Process: Incorporating Local and Global Event Contexts](https://mlsanity.com/paper/2306.14072/) (2023)
- [TS-Diffusion: Generating Highly Complex Time Series with Diffusion Models](https://mlsanity.com/paper/2311.03303/) (2023)
- [Interval-censored Hawkes processes](https://mlsanity.com/paper/2104.07932/) (2021)
- [Neural Spatiotemporal Point Processes: Trends and Challenges](https://mlsanity.com/paper/2502.09341/) (2025)
- [Understanding the Spread of COVID-19 Epidemic: A Spatio-Temporal Point Process View](https://mlsanity.com/paper/2106.13097/) (2021)
- [Bayesian Neural Hawkes Process for Event Uncertainty Prediction](https://mlsanity.com/paper/2112.14474/) (2021)
- [Discovering Intrinsic Spatial-Temporal Logic Rules to Explain Human Actions](https://mlsanity.com/paper/2306.12244/) (2023)
- [Flexible Parametric Inference for Space-Time Hawkes Processes](https://mlsanity.com/paper/2406.06849/) (2024)
- [A Spatio-Temporal Point Process for Fine-Grained Modeling of Reading Behavior](https://mlsanity.com/paper/2506.19999/) (2025)
- [Scalable Marked Point Processes for Exchangeable and Non-Exchangeable Event Sequences](https://mlsanity.com/paper/2105.14574/) (2021)
- [Hierarchical Probabilistic Conformal Prediction for Distributed Energy Resources Adoption](https://mlsanity.com/paper/2411.12193/) (2024)
- [Fine-grained Spatio-temporal Event Prediction with Self-adaptive Anchor Graph](https://mlsanity.com/paper/2501.08653/) (2025)
- [Cox-Hawkes: doubly stochastic spatiotemporal Poisson processes](https://mlsanity.com/paper/2210.11844/) (2022)
- [New User Event Prediction Through the Lens of Causal Inference](https://mlsanity.com/paper/2407.05625/) (2024)
- [Likelihood-Free Estimation for Spatiotemporal Hawkes processes with missing data and application to predictive policing](https://mlsanity.com/paper/2502.07111/) (2025)
- [Deep spatio-temporal point processes: Advances and new directions](https://mlsanity.com/paper/2504.06364/) (2025)
- [Temporal Tokenization Strategies for Event Sequence Modeling with Large Language Models](https://mlsanity.com/paper/2512.13618/) (2025)
- [Score-Based Change-Point Detection and Region Localization for Spatio-Temporal Point Processes](https://mlsanity.com/paper/2602.04798/) (2026)
- [Cascade-Aware Multi-Agent Routing: Spatio-Temporal Sidecars and Geometry-Switching](https://mlsanity.com/paper/2603.17112/) (2026)
- [Imitation Learning of Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/1906.05467/) (2019)

## Abstract (arXiv)

Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in fields where spatio-temporal clustering of events is observed, such as earthquake modeling, infectious disease, and crime. In the past several decades, advances have been made in estimation, inference, simulation, and diagnostic tools for self-exciting point process models. In this review, I describe the basic theory, survey related estimation and inference techniques from each field, highlight several key applications, and suggest directions for future research.