Flexible Parametric Inference for Space-Time Hawkes Processes

• URL: http://arxiv.org/abs/2406.06849v2
• Date: Mon, 17 Jun 2024 13:18:18 GMT
• Title: Flexible Parametric Inference for Space-Time Hawkes Processes
• Authors: Emilia Siviero, Guillaume Staerman, Stephan Clémençon, Thomas Moreau,
• Abstract summary: 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 space-time Hawkes process based on such data.
• Score: 9.21863588989844
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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