Numerically Efficient Parametric Inference for Learning Space-Time Hawkes Processes

In a wide range of spatio-Temporal datasets, from sociology to seismology, self-exciting dynamics are often observed, characterized by event triggering and clustering across both space and time. Space-Time Hawkes processes provide a powerful framework to model such phenomena. This paper introduces a flexible parametric inference method to estimate the underlying kernel parameters involved in the intensity function of a space-Time Hawkes process based on such data. Our approach combines three core components: 1) kernels with finite support, 2) discretization of the space-Time domain, and 3) efficient (possibly approximate) precomputations. The inference method we propose then relies on a gradient-based solver that offers both computational efficiency and strong statistical performance. Alongside a detailed presentation of the algorithmic framework, we present numerical experiments on synthetic and real spatio-Temporal data, offering solid empirical evidence of the validity and applicability of the proposed methodology.