Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

TL;DR

This paper introduces a novel method for uncovering causal structures in multivariate Hawkes processes with hidden subprocesses, using a discrete-time approximation and an iterative algorithm to identify both observed and latent causal influences.

Contribution

It provides the first necessary and sufficient conditions for identifying latent subprocesses and causal influences in Hawkes processes, along with an effective two-phase algorithm for structure learning.

Findings

Successfully recovers causal structures in synthetic data

Effectively uncovers latent subprocesses in real-world datasets

Outperforms existing methods in causal inference accuracy

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.