Flexible Parametric Inference for Space-Time Hawkes Processes
<|reference_start|>Flexible Parametric Inference for Space-Time Hawkes Processes: Many modern spatio-temporal data sets, in sociology, epidemiology or seismology, for example, exhibit self-exciting characteristics, triggering and clustering behaviors both at the same time, that a suitable Hawkes space-time process can accurately capture. This paper aims to develop a fast and flexible parametric inference technique to recover the parameters of the kernel functions involved in the intensity function of a space-time Hawkes process based on such data. Our statistical approach combines three key ingredients: 1) kernels with finite support are considered, 2) the space-time domain is appropriately discretized, and 3) (approximate) precomputations are used. The inference technique we propose then consists of a $\ell_2$ gradient-based solver that is fast and statistically accurate. In addition to describing the algorithmic aspects, numerical experiments have been carried out on synthetic and real spatio-temporal data, providing solid empirical evidence of the relevance of the proposed methodology.<|reference_end|>
@article{siviero2024flexible,
    title={Flexible Parametric Inference for Space-Time Hawkes Processes},
    author={Emilia Siviero, Guillaume Staerman, Stephan Cl'emenc{c}on, Thomas
  Moreau},
    journal={arXiv preprint arXiv:2406.06849},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.06849},
    primaryClass={stat.ML cs.LG}
}