# Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes

arXiv: https://arxiv.org/abs/2402.04740 · HTML: https://mlsanity.com/paper/2402.04740/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 6 of 6)

- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [TiDeH: Time-Dependent Hawkes Process for Predicting Retweet Dynamics](https://mlsanity.com/paper/1603.09449/) (2016)
- [Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction](https://mlsanity.com/paper/1811.06321/) (2018)
- [Shallow Neural Hawkes: Non-parametric kernel estimation for Hawkes processes](https://mlsanity.com/paper/2006.02460/) (2020)
- [A neural network based model for multi-dimensional nonlinear Hawkes processes](https://mlsanity.com/paper/2303.03073/) (2023)

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

- [Nonparametric estimation of Hawkes processes with RKHSs](https://mlsanity.com/paper/2411.00621/) (2024)

## Abstract (arXiv)

An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive literature has been dedicated to the non-parametric estimation of both the linear and non-linear Hawkes process, there remains a significant gap in the literature regarding the marked Hawkes process. In response to this, we propose a methodology for estimating the conditional intensity of the marked Hawkes process. We introduce two distinct models: textitShallow Neural Hawkes with marks- for Hawkes processes with excitatory kernels and textitNeural Network for Non-Linear Hawkes with Marks- for non-linear Hawkes processes. Both these approaches take the past arrival times and their corresponding marks as the input to obtain the arrival intensity. This approach is entirely non-parametric, preserving the interpretability associated with the marked Hawkes process. To validate the efficacy of our method, we subject the method to synthetic datasets with known ground truth. Additionally, we apply our method to model cryptocurrency order book data, demonstrating its applicability to real-world scenarios.