Multivariate Spatio-Temporal Neural Hawkes Processes

2026-02-27

AI Summary

Existing neural Hawkes processes struggle to effectively model the complex spatiotemporal dynamics in multivariate event data, particularly in capturing spatial dependencies and interactions among multiple event types. This work proposes a multivariate spatiotemporal neural Hawkes process that, for the first time, incorporates a learnable spatial decay mechanism to integrate spatial information into the evolution of latent states. Coupled with a flexible temporal decay function, the model captures both excitatory and inhibitory effects without requiring predefined triggering kernels. On synthetic data, the method accurately recovers the underlying spatiotemporal intensity structure and significantly outperforms purely temporal models. When applied to real-world terrorist attack data from Pakistan, it successfully uncovers intricate spatiotemporal interactions across event types, while also highlighting the limitations of relying solely on likelihood-based evaluation metrics.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Multivariate
• Spatio-Temporal
• Neural Hawkes Process
• Point Processes
• Event Data

Innovation

• Spatio-Temporal Modeling
• Neural Hawkes Process
• Multivariate Point Processes
• Learnable Decay Dynamics
• Intensity Function