# A neural network based model for multi-dimensional nonlinear Hawkes processes

arXiv: https://arxiv.org/abs/2303.03073 · HTML: https://mlsanity.com/paper/2303.03073/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 53 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity](https://mlsanity.com/paper/2205.04107/) (2022)
- [Interacting Hawkes processes with multiplicative inhibition](https://mlsanity.com/paper/2105.10597/) (2021)
- [Multivariate Hawkes Processes for Large-scale Inference](https://mlsanity.com/paper/1602.08418/) (2016)
- [Maximum Likelihood Estimation for Hawkes Processes with self-excitation or inhibition](https://mlsanity.com/paper/2103.05299/) (2021)
- [Hawkes Processes with Stochastic Excitations](https://mlsanity.com/paper/1609.06831/) (2016)
- [Gradient-based estimation of linear Hawkes processes with general kernels](https://mlsanity.com/paper/2111.10637/) (2021)
- [Second order statistics characterization of Hawkes processes and non-parametric estimation](https://mlsanity.com/paper/1401.0903/) (2014)
- [Shallow Neural Hawkes: Non-parametric kernel estimation for Hawkes processes](https://mlsanity.com/paper/2006.02460/) (2020)

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

- [Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes](https://mlsanity.com/paper/2402.04740/) (2024)

## Abstract (arXiv)

This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit both mutually-exciting and inhibitive patterns. The NNNH approach models the individual kernels and the base intensity of the nonlinear Hawkes process using feed forward neural networks and jointly calibrates the parameters of the networks by maximizing the log-likelihood function. We utilize Stochastic Gradient Descent to search for the optimal parameters and propose an unbiased estimator for the gradient, as well as an efficient computation method. We demonstrate the flexibility and accuracy of our method through numerical experiments on both simulated and real-world data, and compare it with state-of-the-art methods. Our results highlight the effectiveness of the NNNH method in accurately capturing the complexities of nonlinear Hawkes processes.