Learning Neural Jump Stochastic Differential Equations with Latent Graph for Multivariate Temporal Point Processes

Abstract

Multivariate Temporal Point Processes (MTPPs) play an important role in diverse domains such as social networks and finance for predicting event sequence data. In recent years, MTPPs based on Ordinary Differential Equations (ODEs) and Stochastic Differential Equations (SDEs) have demonstrated their strong modeling capabilities. However, these models have yet to thoroughly consider the underlying relationships among different event types to enhance their modeling capacity. Therefore, this paper introduces a method that uses neural SDEs with a jump process guided by the latent graph. Firstly, our proposed method employs multi-dimensional SDEs to capture the dynamics of the intensity function for each event type. Subsequently, a latent graph structure is integrated into the jump process without any encoder, aiming to enhance the modeling and predictive capabilities for MTPPs. Theoretical analysis guarantees the existence and uniqueness of the solution for our proposed method. The experiments conducted on multiple real-world datasets show that our approaches demonstrate significant competitiveness when compared to state-of-the-art neural point processes. Meanwhile, the trainable parameters of the latent graph also improve the model interpretability without any prior knowledge. Our code is available at https://github.com/cgao-comp/LNJSDE.