Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks
This addresses a challenge in modeling real-world event-driven systems with partial observations, representing an incremental advance over existing methods focused on observed subprocesses.
The paper tackles the problem of learning causal structures in Hawkes processes when latent subprocesses are present, by establishing identifiability conditions and proposing a two-phase iterative algorithm that recovers these structures effectively in experiments.
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.