# Maximum Likelihood Estimation for Hawkes Processes with self-excitation or inhibition

arXiv: https://arxiv.org/abs/2103.05299 · HTML: https://mlsanity.com/paper/2103.05299/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 9 Mar 2021.

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

- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Feature Driven and Point Process Approaches for Popularity Prediction](https://mlsanity.com/paper/1608.04862/) (2016)
- [SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model Diffusions in Finite Populations](https://mlsanity.com/paper/1711.01679/) (2017)
- [A Tutorial on Hawkes Processes for Events in Social Media](https://mlsanity.com/paper/1708.06401/) (2017)
- [The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation](https://mlsanity.com/paper/1707.04928/) (2017)
- [Second order statistics characterization of Hawkes processes and non-parametric estimation](https://mlsanity.com/paper/1401.0903/) (2014)

## Built on by (most cited first, 5 of 5)

- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [Scalable Marked Point Processes for Exchangeable and Non-Exchangeable Event Sequences](https://mlsanity.com/paper/2105.14574/) (2021)
- [A neural network based model for multi-dimensional nonlinear Hawkes processes](https://mlsanity.com/paper/2303.03073/) (2023)
- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)
- [Latent Factor Point Processes for Patient Representation in Electronic Health Records](https://mlsanity.com/paper/2508.20327/) (2025)

## Abstract (arXiv)

In this paper, we present a maximum likelihood method for estimating the parameters of a univariate Hawkes process with self-excitation or inhibition. Our work generalizes techniques and results that were restricted to the self-exciting scenario. The proposed estimator is implemented for the classical exponential kernel and we show that, in the inhibition context, our procedure provides more accurate estimations than current alternative approaches.