A0485
Title: Flexible inference for spatiotemporal Hawkes processes with general parametric kernels
Authors: Emilia Siviero - Telecom Paris (France) [presenting]
Guillaume Staerman - Inria, Universite Paris-Saclay (France)
Stephan Clemencon - Telecom Paris (France)
Thomas Moreau - Inria - Universite Paris-Saclay (France)
Abstract: With advancements in data collection technologies, fields such as sociology, epidemiology, and seismology are increasingly encountering spatiotemporal datasets with self-exciting properties characterized by triggering and clustering behaviors that can be effectively modeled using a Hawkes space-time process. A fast and flexible parametric inference method is developed to estimate the parameters of the kernel functions in the intensity function of a space-time Hawkes process based on such data. The statistical approach integrates three main components: 1) the use of kernels with finite support, 2) appropriate discretization of the space-time domain, and 3) the use of (approximate) precomputations. The proposed inference technique employs an $\ell_2$ gradient-based solver, which is both fast and statistically accurate. In addition to describing the algorithmic aspects, numerical experiments have been carried out on synthetic and real spatiotemporal data, providing solid empirical evidence of the relevance of the proposed methodology.
