# Gradient-based estimation of linear Hawkes processes with general kernels

arXiv: https://arxiv.org/abs/2111.10637 · HTML: https://mlsanity.com/paper/2111.10637/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2021.

## Built on by (most cited first, 4 of 4)

- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [A neural network based model for multi-dimensional nonlinear Hawkes processes](https://mlsanity.com/paper/2303.03073/) (2023)
- [Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions](https://mlsanity.com/paper/2608.19151/) (2026)
- [Estimation of an Order Book Dependent Hawkes Process for Large Datasets](https://mlsanity.com/paper/2307.09077/) (2023)

## Abstract (arXiv)

Linear multivariate Hawkes processes (MHP) are a fundamental class of point processes with self-excitation. When estimating parameters for these processes, a difficulty is that the two main error functionals, the log-likelihood and the least squares error (LSE), as well as the evaluation of their gradients, have a quadratic complexity in the number of observed events. In practice, this prohibits the use of exact gradient-based algorithms for parameter estimation. We construct an adaptive stratified sampling estimator of the gradient of the LSE. This results in a fast parametric estimation method for MHP with general kernels, applicable to large datasets, which compares favourably with existing methods.