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

Area of Science:

• Computational Statistics
• Machine Learning
• Point Processes

Background:

• Hawkes processes traditionally model time-continuous events with history dependence.
• Existing models often lack flexibility or require substantial data for accurate parameterization.

Purpose of the Study:

• To propose an extended Hawkes process model with flexible, Gaussian Process-based self-excitation and inhibition.
• To develop a Bayesian inference framework for this enhanced model, suitable for scarce data scenarios.

Main Methods:

• Formulation of an extended Hawkes process with Gaussian Process self-effects.
• Derivation of a Bayesian inference algorithm using an aggregated sum of Gaussian Processes.
• Application of data augmentation and mean-field variational inference for parameter learning.

Main Results:

• The proposed model offers enhanced flexibility compared to traditional parameterizations.
• The Bayesian inference approach facilitates effective learning even with limited datasets.
• Methodology demonstrated on diverse datasets, showing competitive or superior performance.

Conclusions:

• The developed Gaussian Process-enhanced Hawkes process provides a flexible and data-efficient approach for modeling history-dependent point processes.
• The Bayesian inference framework is robust and applicable across various domains.
• This work advances the state-of-the-art in statistical modeling of event data.