Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

Songyao Jin; Biwei Huang

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arXiv · 2508.11727

Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

Songyao Jin·Biwei Huang

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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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Songyao Jin, Biwei Huang. 2025-08-15. Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks. https://arxiv.org/abs/2508.11727

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