Flexible Parametric Inference for Space-Time Hawkes Processes

TL;DR

This paper introduces a fast, flexible parametric inference method for space-time Hawkes processes, effectively capturing self-exciting clustering in complex spatio-temporal data sets.

Contribution

It develops a novel inference technique combining finite support kernels, domain discretization, and precomputations, enabling efficient parameter recovery for space-time Hawkes models.

Findings

Method is fast and statistically accurate

Effective on synthetic and real data

Outperforms existing inference techniques

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.