Conjugate Bayesian Two-step Change Point Detection for Hawkes Process

TL;DR

This paper introduces a conjugate Bayesian two-step change point detection method for Hawkes processes, significantly improving computational efficiency and accuracy over existing non-conjugate approaches through data augmentation.

Contribution

It develops a conjugate Bayesian approach for change point detection in Hawkes processes, enabling analytical solutions and faster inference compared to prior non-conjugate methods.

Findings

Outperforms baseline methods in synthetic data experiments

Demonstrates superior accuracy and efficiency on real data

Shows robustness to hyperparameter variations

Abstract

The Bayesian two-step change point detection method is popular for the Hawkes process due to its simplicity and intuitiveness. However, the non-conjugacy between the point process likelihood and the prior requires most existing Bayesian two-step change point detection methods to rely on non-conjugate inference methods. These methods lack analytical expressions, leading to low computational efficiency and impeding timely change point detection. To address this issue, this work employs data augmentation to propose a conjugate Bayesian two-step change point detection method for the Hawkes process, which proves to be more accurate and efficient. Extensive experiments on both synthetic and real data demonstrate the superior effectiveness and efficiency of our method compared to baseline methods. Additionally, we conduct ablation studies to explore the robustness of our method concerning various hyperparameters. Our code is publicly available at https://github.com/Aurora2050/CoBay-CPD.