# Efficient EM-Variational Inference for Hawkes Process

arXiv: https://arxiv.org/abs/1905.12251 · HTML: https://mlsanity.com/paper/1905.12251/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

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

- [Deep Neyman-Scott Processes](https://mlsanity.com/paper/2111.03949/) (2021)
- [Nonlinear Hawkes Processes in Time-Varying System](https://mlsanity.com/paper/2106.04844/) (2021)
- [Bayesian Neural Hawkes Process for Event Uncertainty Prediction](https://mlsanity.com/paper/2112.14474/) (2021)
- [Nonlinear Hawkes Process with Gaussian Process Self Effects](https://mlsanity.com/paper/2105.09618/) (2021)

## Abstract (arXiv)

In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric model, namely Gaussian process modulated Hawkes process and propose an EM-variational inference scheme. In this model, a transformation of Gaussian process is used as a prior on the baseline intensity and triggering kernel. By introducing a latent branching structure, the inference of baseline intensity and triggering kernel is decoupled and the variational inference scheme is embedded into an EM framework naturally. We also provide a series of schemes to accelerate the inference. Results of synthetic and real data experiments show that the underlying baseline intensity and triggering kernel can be recovered without parametric restriction and our Bayesian nonparametric estimation is superior to other state of the arts.