# Flexible Parametric Inference for Space-Time Hawkes Processes

arXiv: https://arxiv.org/abs/2406.06849 · HTML: https://mlsanity.com/paper/2406.06849/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 8 of 8)

- [A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications](https://mlsanity.com/paper/1708.02647/) (2017)
- [Sparse and low-rank multivariate Hawkes processes](https://mlsanity.com/paper/1501.00725/) (2015)
- [Spatial-Temporal-Textual Point Processes for Crime Linkage Detection](https://mlsanity.com/paper/1902.00440/) (2019)
- [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)
- [FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels](https://mlsanity.com/paper/2210.04635/) (2022)
- [Modeling of Spatio-Temporal Hawkes Processes with Randomized Kernels](https://mlsanity.com/paper/2003.03671/) (2020)
- [Tensor Kernel Recovery for Spatio-Temporal Hawkes Processes](https://mlsanity.com/paper/2011.12151/) (2020)

## Built on by (most cited first, 3 of 3)

- [EarthquakeNPP: A Benchmark for Earthquake Forecasting with Neural Point Processes](https://mlsanity.com/paper/2410.08226/) (2024)
- [Nonparametric estimation of Hawkes processes with RKHSs](https://mlsanity.com/paper/2411.00621/) (2024)
- [Multivariate Spatio-Temporal Neural Hawkes Processes](https://mlsanity.com/paper/2602.23629/) (2026)

## Abstract (arXiv)

Many modern spatio-temporal data sets, in sociology, epidemiology or seismology, for example, exhibit self-exciting characteristics, triggering and clustering behaviors both at the same time, that a suitable Hawkes space-time process can accurately capture. This paper aims to develop a fast and flexible parametric inference technique to recover the parameters of the kernel functions involved in the intensity function of a space-time Hawkes process based on such data. Our statistical approach combines three key ingredients: 1) kernels with finite support are considered, 2) the space-time domain is appropriately discretized, and 3) (approximate) precomputations are used. The inference technique we propose then consists of a ℓ2 gradient-based solver that is fast and statistically accurate. In addition to describing the algorithmic aspects, numerical experiments have been carried out on synthetic and real spatio-temporal data, providing solid empirical evidence of the relevance of the proposed methodology.