Title: Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks
Primary area: causal reasoning
Keywords: Hawkes processes, causal discovery, latent subprocess model, structure learning, time series

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.

TL;DR: We propose a method to uncover causal relationships in partially observed multivariate Hawkes processes, despite the presence of latent subprocesses, using a discrete-time representation and a two-phase iterative algorithm.