# Spatio-temporal point processes with deep non-stationary kernels

arXiv: https://arxiv.org/abs/2211.11179 · HTML: https://mlsanity.com/paper/2211.11179/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [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)
- [A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications](https://mlsanity.com/paper/1708.02647/) (2017)
- [Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1807.09331/) (2018)
- [Spatial-Temporal-Textual Point Processes for Crime Linkage Detection](https://mlsanity.com/paper/1902.00440/) (2019)
- [Neural Spectral Marked Point Processes](https://mlsanity.com/paper/2106.10773/) (2021)
- [Dynamic Hawkes Processes for Discovering Time-evolving Communities' States behind Diffusion Processes](https://mlsanity.com/paper/2105.11152/) (2021)
- [A recursive point process model for infectious diseases](https://mlsanity.com/paper/1703.08202/) (2017)

## Built on by (most cited first, 8 of 8)

- [Conditional Generative Modeling for High-dimensional Marked Temporal Point Processes](https://mlsanity.com/paper/2305.12569/) (2023)
- [Neural Spatiotemporal Point Processes: Trends and Challenges](https://mlsanity.com/paper/2502.09341/) (2025)
- [EarthquakeNPP: A Benchmark for Earthquake Forecasting with Neural Point Processes](https://mlsanity.com/paper/2410.08226/) (2024)
- [Score Matching-based Pseudolikelihood Estimation of Neural Marked Spatio-Temporal Point Process with Uncertainty Quantification](https://mlsanity.com/paper/2310.16310/) (2023)
- [Deep spatio-temporal point processes: Advances and new directions](https://mlsanity.com/paper/2504.06364/) (2025)
- [GreenTEA: Gradient Descent with Topic-modeling and Evolutionary Auto-prompting](https://mlsanity.com/paper/2508.16603/) (2025)
- [Multivariate Spatio-Temporal Neural Hawkes Processes](https://mlsanity.com/paper/2602.23629/) (2026)
- [LLM-Guided Transportation Hub Capacity Planning with Textual Business Inputs](https://mlsanity.com/paper/2607.03651/) (2026)

## Abstract (arXiv)

Point process data are becoming ubiquitous in modern applications, such as social networks, health care, and finance. Despite the powerful expressiveness of the popular recurrent neural network (RNN) models for point process data, they may not successfully capture sophisticated non-stationary dependencies in the data due to their recurrent structures. Another popular type of deep model for point process data is based on representing the influence kernel (rather than the intensity function) by neural networks. We take the latter approach and develop a new deep non-stationary influence kernel that can model non-stationary spatio-temporal point processes. The main idea is to approximate the influence kernel with a novel and general low-rank decomposition, enabling efficient representation through deep neural networks and computational efficiency and better performance. We also take a new approach to maintain the non-negativity constraint of the conditional intensity by introducing a log-barrier penalty. We demonstrate our proposed method's good performance and computational efficiency compared with the state-of-the-art on simulated and real data.