Multivariate Spatio-Temporal Neural Hawkes Processes

TL;DR

This paper introduces a neural Hawkes process model that captures complex multivariate spatio-temporal event dynamics, improving over existing models by integrating spatial information and revealing new insights into intensity behaviors.

Contribution

The paper extends neural Hawkes processes by incorporating spatial dynamics, enabling flexible modeling of excitation and inhibition in multivariate spatio-temporal data.

Findings

Successfully recovers spatial and temporal intensity structures in simulations.

Outperforms existing temporal neural Hawkes models in capturing spatio-temporal patterns.

Effectively models terrorism event data, revealing complex interactions.

Abstract

We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial information into latent state evolution through learned temporal and spatial decay dynamics, enabling flexible modeling of excitation and inhibition without predefined triggering kernels. By analyzing fitted intensity functions of deep learning-based temporal Hawkes process models, we identify a modeling gap in how fitted intensity behavior is captured beyond likelihood-based performance, which motivates the proposed spatio-temporal approach. Simulation studies show that the proposed method successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns, while existing temporal neural Hawkes process approach fails to do so. An application to terrorism data from Pakistan further demonstrates the proposed model's ability to capture complex spatio-temporal interaction across multiple event types.