Geometric Hawkes Processes with Graph Convolutional Recurrent Neural Networks

Abstract

Hawkes processes are popular for modeling correlated temporal sequences that exhibit mutual-excitation properties. Existing approaches such as feature-enriched processes or variations of Multivariate Hawkes processes either fail to describe the exact mutual influence between sequences or become computational inhibitive in most real-world applications involving large dimensions. Incorporating additional geometric structure in the form of graphs into Hawkes processes is an effective and efficient way for improving model prediction accuracy. In this paper, we propose the Geometric Hawkes Process (GHP) model to better correlate individual processes, by integrating Hawkes processes and a graph convolutional recurrent neural network. The deep network structure is computational efficient since it requires constant parameters that are independent of the graph size. The experiment results on real-world data show that our framework outperforms recent state-of-art methods.