# Efficient Non-parametric Bayesian Hawkes Processes

@inproceedings{Zhang2019EfficientNB, title={Efficient Non-parametric Bayesian Hawkes Processes}, author={Rui Zhang and Christian J. Walder and Marian-Andrei Rizoiu and Lexing Xie}, booktitle={IJCAI}, year={2019} }

In this paper, we develop an efficient non-parametric 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 stationarity of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We…

## 26 Citations

Sparse Gaussian Process Modulated Hawkes Process

- Computer ScienceArXiv
- 2019

This paper proposes a new non-parametric Bayesian Hawkes process whose triggering kernel is modeled as a squared sparse Gaussian process and presents the variational inference scheme for the model optimization, which has the advantage of linear time complexity by leveraging the stationarity of the triggering kernel.

Efficient Inference for Nonparametric Hawkes Processes Using Auxiliary Latent Variables

- Computer Science
- 2020

The baseline intensity and triggering kernel are both modeled as the sigmoid transformation of random trajectories drawn from a GP as well as an efficient mean-field variational inference algorithm to approximate the posterior and a sparse GP approximation is introduced to reduce complexity.

Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

- Computer ScienceEntropy
- 2022

This work proposes an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process, and describes a mean-field variational inference approach to learn the model parameters.

Nonlinear Hawkes Processes in Time-Varying System

- Computer ScienceArXiv
- 2021

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.

Deep Neyman-Scott Processes

- Computer ScienceAISTATS
- 2022

A deep Neyman-Scott process is considered, for which the building components of a network are all Poisson processes, and an e-cient posterior sampling via Markov chain Monte Carlo is developed, which opens up room for the inference in sophisti-cated hierarchical point processes.

Interval-censored Hawkes processes

- MathematicsArXiv
- 2021

The Mean Behavior Poisson (MBP) process is defined, a novel Poisson process with a direct parameter correspondence to the popular self-exciting Hawkes process and it is shown that on real-world datasets that the MBP process outperforms HIP for the task of popularity prediction.

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

- MathematicsStat. Comput.
- 2022

This work introduces a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior and demonstrates the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters.

THP: Topological Hawkes Processes for Learning Granger Causality on Event Sequences

- Computer ScienceArXiv
- 2021

A Topological Hawkes processes (THP) is proposed to draw a connection between the graph convolution in topology domain and the temporal Convolution in time domains and the Granger causality learning method on THP in a likelihood framework is proposed.

THPs: Topological Hawkes Processes for Learning Causal Structure on Event Sequences.

- Computer ScienceIEEE transactions on neural networks and learning systems
- 2022

A topological Hawkes process (THP) is proposed to draw a connection between the graph convolution in the topology domain and the temporal Convolution in time domains to learn causal structure learning on THP in a likelihood framework.

Flexible Temporal Point Processes Modeling with Nonlinear Hawkes Processes with Gaussian Processes Excitations and Inhibitions

- Computer Science
- 2021

An extended Hawkes process model where the self–effects are of both excitatory and inhibitory type and follow a Gaussian Process is proposed, and efficient approximate Bayesian inference is achieved via data augmentation, and a mean–field variational inference approach is described to learn the model parameters.

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