# Nonlinear Hawkes Process with Gaussian Process Self Effects

arXiv: https://arxiv.org/abs/2105.09618 · HTML: https://mlsanity.com/paper/2105.09618/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 20 May 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes](https://mlsanity.com/paper/1808.00831/) (2018)
- [Efficient Non-parametric Bayesian Hawkes Processes](https://mlsanity.com/paper/1810.03730/) (2018)
- [Efficient Bayesian Inference for a Gaussian Process Density Model](https://mlsanity.com/paper/1805.11494/) (2018)
- [Efficient EM-Variational Inference for Hawkes Process](https://mlsanity.com/paper/1905.12251/) (2019)

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

- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)

## Abstract (arXiv)

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and our approach dispenses with the necessity of estimating a branching structure for the posterior, as we perform inference on an aggregated sum of Gaussian Processes. Efficient approximate Bayesian inference is achieved via data augmentation, and we describe a mean--field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from three different domains and compare it to previously reported results.