# Efficient Non-parametric Bayesian Hawkes Processes

arXiv: https://arxiv.org/abs/1810.03730 · HTML: https://mlsanity.com/paper/1810.03730/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2018.

## Built on by (most cited first, 15 of 15)

- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Deep Neyman-Scott Processes](https://mlsanity.com/paper/2111.03949/) (2021)
- [Before It's Too Late: A State Space Model for the Early Prediction of Misinformation and Disinformation Engagement](https://mlsanity.com/paper/2502.04655/) (2025)
- [Interval-censored Hawkes processes](https://mlsanity.com/paper/2104.07932/) (2021)
- [FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels](https://mlsanity.com/paper/2210.04635/) (2022)
- [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)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Conjugate Bayesian Two-step Change Point Detection for Hawkes Process](https://mlsanity.com/paper/2409.17591/) (2024)
- [Nonparametric estimation of Hawkes processes with RKHSs](https://mlsanity.com/paper/2411.00621/) (2024)
- [Nonlinear Hawkes Process with Gaussian Process Self Effects](https://mlsanity.com/paper/2105.09618/) (2021)
- [Row-clustering of a Point Process-valued Matrix](https://mlsanity.com/paper/2110.01207/) (2021)
- [Fine-Grained ε-Margin Closed-Form Stabilization of Parametric Hawkes Processes](https://mlsanity.com/paper/2105.03800/) (2021)
- [Spatio-temporal extreme event modeling of terror insurgencies](https://mlsanity.com/paper/2110.08363/) (2021)
- [Uncovering Social Network Activity Using Joint User and Topic Interaction](https://mlsanity.com/paper/2506.12842/) (2025)

## Abstract (arXiv)

In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the finite support assumption of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms -- a block Gibbs sampler and a maximum a posteriori estimator based on expectation maximization -- and we show that our methods have a linear time complexity, both theoretically and empirically. On synthetic data, we show our methods to be able to infer flexible Hawkes triggering kernels. On two large-scale Twitter diffusion datasets, we show that our methods outperform the current state-of-the-art in goodness-of-fit and that the time complexity is linear in the size of the dataset. We also observe that on diffusions related to online videos, the learned kernels reflect the perceived longevity for different content types such as music or pets videos.