# Multivariate Spatio-Temporal Neural Hawkes Processes

arXiv: https://arxiv.org/abs/2602.23629 · HTML: https://mlsanity.com/paper/2602.23629/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [EasyTPP: Towards Open Benchmarking Temporal Point Processes](https://mlsanity.com/paper/2307.08097/) (2023)
- [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)
- [Spatio-temporal point processes with deep non-stationary kernels](https://mlsanity.com/paper/2211.11179/) (2022)
- [Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction](https://mlsanity.com/paper/1811.06321/) (2018)
- [Flexible Spatio-Temporal Hawkes Process Models for Earthquake Occurrences](https://mlsanity.com/paper/2210.08053/) (2022)
- [Transformers versus LSTMs for electronic trading](https://mlsanity.com/paper/2309.11400/) (2023)
- [Flexible Parametric Inference for Space-Time Hawkes Processes](https://mlsanity.com/paper/2406.06849/) (2024)
- [Flexible multivariate spatio-temporal Hawkes process models of terrorism](https://mlsanity.com/paper/2202.12346/) (2022)
- [Likelihood-Free Estimation for Spatiotemporal Hawkes processes with missing data and application to predictive policing](https://mlsanity.com/paper/2502.07111/) (2025)

## Abstract (arXiv)

We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial information into latent state evolution through learned temporal and spatial decay dynamics, enabling flexible modeling of excitation and inhibition without predefined triggering kernels. By analyzing fitted intensity functions of deep learning-based temporal Hawkes process models, we identify a modeling gap in how fitted intensity behavior is captured beyond likelihood-based performance, which motivates the proposed spatio-temporal approach. Simulation studies show that the proposed method successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns, while existing temporal neural Hawkes process approach fails to do so. An application to terrorism data from Pakistan further demonstrates the proposed model's ability to capture complex spatio-temporal interaction across multiple event types.