Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

• URL: http://arxiv.org/abs/2508.11727v2
• Date: Thu, 25 Sep 2025 09:58:04 GMT
• Title: Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks
• Authors: Songyao Jin, Biwei Huang,
• Abstract summary: We show that continuous-time event sequences can be represented by a discrete-time causal model as the time interval shrinks.<n>We propose a two-phase iterative algorithm that alternates between inferring causal relationships among discovered subprocesses and uncovering new latent subprocesses.
• Score: 23.669083610595838
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 causal 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.

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