Fused Gromov-Wasserstein Alignment for Hawkes Processes
This addresses the problem of aligning event types in Hawkes processes for researchers in machine learning and statistics, but it appears incremental as it builds on existing Gromov-Wasserstein and Hawkes process methods.
The paper tackles the problem of aligning event types between Hawkes processes in different event spaces by proposing a fused Gromov-Wasserstein alignment method, which jointly learns the processes and their optimal transport via maximum likelihood estimation with a regularizer, and experimental results show it works well on synthetic and real-world data.
We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure their dissimilarity, which considers both the Wasserstein discrepancy based on their base intensities and the Gromov-Wasserstein discrepancy based on their infectivity matrices. Accordingly, the learned optimal transport reflects the correspondence between the event types of these two Hawkes processes. The Hawkes processes and their optimal transport are learned jointly via maximum likelihood estimation, with a fused Gromov-Wasserstein regularizer. Experimental results show that the proposed method works well on synthetic and real-world data.