# Deep spatio-temporal point processes: Advances and new directions

arXiv: https://arxiv.org/abs/2504.06364 · HTML: https://mlsanity.com/paper/2504.06364/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 88 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 30 of 42)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [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)
- [A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications](https://mlsanity.com/paper/1708.02647/) (2017)
- [Neural Temporal Point Processes For Modelling Electronic Health Records](https://mlsanity.com/paper/2007.13794/) (2020)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Modeling Event Propagation via Graph Biased Temporal Point Process](https://mlsanity.com/paper/1908.01623/) (2019)
- [Deep Mixture Point Processes: Spatio-temporal Event Prediction with Rich Contextual Information](https://mlsanity.com/paper/1906.08952/) (2019)
- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1807.09331/) (2018)
- [Automatic Integration for Spatiotemporal Neural Point Processes](https://mlsanity.com/paper/2310.06179/) (2023)
- [Spatio-Temporal Graph Neural Point Process for Traffic Congestion Event Prediction](https://mlsanity.com/paper/2311.08635/) (2023)
- [Spatial-Temporal-Textual Point Processes for Crime Linkage Detection](https://mlsanity.com/paper/1902.00440/) (2019)
- [Spatio-Temporal Point Processes with Attention for Traffic Congestion Event Modeling](https://mlsanity.com/paper/2005.08665/) (2020)
- [Neural Spectral Marked Point Processes](https://mlsanity.com/paper/2106.10773/) (2021)
- [Transformer-Based Neural Marked Spatio Temporal Point Process Model for Football Match Events Analysis](https://mlsanity.com/paper/2302.09276/) (2023)
- [A space-time conditional intensity model for invasive meningococcal disease occurrence](https://mlsanity.com/paper/1508.05740/) (2015)
- [Group Network Hawkes Process](https://mlsanity.com/paper/2002.08521/) (2020)

## Built on by (most cited first, 1 of 1)

- [GreenTEA: Gradient Descent with Topic-modeling and Evolutionary Auto-prompting](https://mlsanity.com/paper/2508.16603/) (2025)

## Abstract (arXiv)

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.