Flexible Parametric Inference for Space-Time Hawkes Processes
This work addresses the need for efficient parameter estimation in self-exciting spatio-temporal models, which is incremental as it builds on existing Hawkes process methods with computational improvements.
The paper tackled the problem of inferring parameters for space-time Hawkes processes from spatio-temporal data by developing a fast and flexible parametric inference technique, achieving statistically accurate results through numerical experiments on synthetic and real data.
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.