# Nonlinear Hawkes Processes in Time-Varying System

arXiv: https://arxiv.org/abs/2106.04844 · HTML: https://mlsanity.com/paper/2106.04844/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 41 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 7 of 7)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [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, 3 of 3)

- [One-hot Generalized Linear Model for Switching Brain State Discovery](https://mlsanity.com/paper/2310.15263/) (2023)
- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)
- [Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes](https://mlsanity.com/paper/2305.18412/) (2023)

## Abstract (arXiv)

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to three key hypotheses: parametric, linear and homogeneous. Recent work has attempted to address these limitations separately. This work aims to overcome all three assumptions simultaneously by proposing the flexible state-switching Hawkes processes: a flexible, nonlinear and nonhomogeneous variant where a state process is incorporated to interact with the point processes. The proposed model empowers Hawkes processes to be applied to time-varying systems. For inference, we utilize the latent variable augmentation technique to design two efficient Bayesian inference algorithms: Gibbs sampler and mean-field variational inference, with analytical iterative updates to estimate the posterior. In experiments, our model achieves superior performance compared to the state-of-the-art competitors.