Fast multi-resolution segmentation for nonstationary Hawkes process using cumulants
INTERNATIONAL JOURNAL OF DATA SCIENCE AND ANALYTICS(2020)
摘要
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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关键词
Hawkes process, Nonstationary, Segmentation, Cumulants
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