Inferring Directed Acyclic Graphs from Event Sequences via Learning Gromov-Wasserstein-Regularized Hawkes Processes

Inferring directed acyclic graphs (DAGs) of event types based on observed event sequences aims to discover the causal relationships hidden in events' temporal behaviors, which is crucial in many applications such as earthquake prediction and epidemic spreading. In this study, we propose a novel method to infer DAGs from event sequences, introducing an optimal transport-based regularizer into the maximum likelihood estimation framework of Hawkes process. In particular, the proposed method infers DAGs based on the infectivity matrices associated with Hawkes processes. A Gromov-Wasserstein distance-based regularizer is applied to penalize the discrepancy between the infectivity matrices and adaptive lower-triangular matrices, ensuring the graphs corresponding to the learned infectivity matrices are directed acyclic. Experiments demonstrate that learning Gromov-Wasserstein-regularized Hawkes processes (HP-GWR) can infer the DAGs robustly from event sequences, whose performance is competitive to state-of-the-art DAG inference methods.