Fast multi-resolution segmentation for nonstationary Hawkes process using cumulants
- Publisher:
- Springer Science and Business Media LLC
- Publication Type:
- Journal Article
- Citation:
- International Journal of Data Science and Analytics, 2020, 10, (4), pp. 321-330
- Issue Date:
- 2020-10-01
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Filename | Description | Size | |||
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Zhou2020_Article_FastMulti-resolutionSegmentati.pdf | Published version | 1.79 MB |
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© 2020, Springer Nature Switzerland AG. The stationarity is assumed in the 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 the 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 hyperparameter, we propose a refined Gaussian process-based segmentation algorithm, which is proved to be a robust method. The proposed algorithm is applied to a real vehicle collision dataset, and the outcome shows some interesting hierarchical dynamic time-varying characteristics.
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