# Fast Multi-resolution Segmentation for Nonstationary Hawkes Process Using Cumulants

## TL;DR

This paper introduces a fast multi-resolution segmentation method for nonstationary Hawkes processes using cumulants, enabling efficient and hierarchical analysis of time-varying event data.

## Contribution

It presents a novel segmentation algorithm based on cumulants that captures nonstationary dynamics and offers a hierarchical view at multiple resolutions.

## Key findings

- Effective segmentation of nonstationary Hawkes processes.
- Hierarchical analysis reveals dynamic time-varying characteristics.
- Robust hyperparameter selection via Gaussian process.

## Abstract

The stationarity is assumed in vanilla Hawkes process, which reduces the model complexity but introduces a strong assumption. In this paper, we propose a fast multi-resolution segmentation algorithm to capture the time-varying characteristics of nonstationary Hawkes process. The proposed algorithm is based on the first and second order cumulants. Except for the computation efficiency, the algorithm can provide a hierarchical view of the segmentation at different resolutions. We extensively investigate the impact of hyperparameters on the performance of this algorithm. To ease the choice of one hyperparameter, a refined Gaussian process based segmentation algorithm is also proposed which proves to be robust. The proposed algorithm is applied to a real vehicle collision dataset and the outcome shows some interesting hierarchical dynamic time-varying characteristics.