Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

2025-08-15

AI Summary

Real-world systems often contain unobserved latent subprocesses, rendering causal structure learning for multivariate Hawkes processes unidentifiable. Method: We establish the first necessary and sufficient conditions for identifying such latent subprocesses and propose a two-stage iterative algorithm based on temporal discretization: Stage I constructs a path-guided initial causal graph over observable variables; Stage II jointly optimizes both the causal relationships among observables and the confounding network linking them to latent subprocesses. The method integrates discretized modeling, path analysis, and structural learning. Contribution/Results: It guarantees theoretical identifiability while enabling simultaneous discovery of causal structure and latent variables. Extensive experiments on synthetic and real-world datasets demonstrate significant improvements over state-of-the-art methods, validating both the theoretical conditions and the algorithm’s robustness.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed subprocesses, real-world systems are often only partially observed, with latent subprocesses posing significant challenges. In this paper, we show that continuous-time event sequences can be represented by a discrete-time model as the time interval shrinks, and we leverage this insight to establish necessary and sufficient conditions for identifying latent subprocesses and the causal influences. Accordingly, we propose a two-phase iterative algorithm that alternates between inferring causal relationships among discovered subprocesses and uncovering new latent subprocesses, guided by path-based conditions that guarantee identifiability. Experiments on both synthetic and real-world datasets show that our method effectively recovers causal structures despite the presence of latent subprocesses.

Problem

• Identifying latent subprocesses in multivariate Hawkes processes
• Establishing conditions for causal influence identifiability
• Recovering causal structures with latent confounders present

Innovation

• Discrete-time model representation for event sequences
• Two-phase iterative algorithm for causal inference
• Path-based conditions ensuring identifiability of latent subprocesses