A Non-stationary Spatiotemporal Hawkes Process for Railway Delay Causality Learning

Accurate causal discovery of railway delay event sequences is crucial for reliable operations in modern complex railway networks, but presents significant challenges due to pronounced non-stationarity and complex network topological dependencies. To address these challenges, we propose the Non-Stationary Spatio-Temporal Self-Attentive Hawkes Process (NSSTHP), a novel framework for learning non-stationary causal structures in railway delay event networks. First, we employ likelihood-based change point detection (PELT) to automatically partition long event sequences into approximately stationary segments. Within each segment, a general spatio-temporally-aware self-attentive Hawkes intensity function is employed for different delay scenarios, which jointly incorporates the spatial topology and temporal dependencies of railway networks under different event delay states. To capture global causal structures, we propose the Symmetric-Balance Thresholding (SBT) method, which adaptively determines the optimal threshold for conversion of real-valued causal matrices to Boolean graphs across segments. Extensive experiments on both synthetic data and real-world datasets demonstrate that NSSTHP significantly outperforms baseline methods in causal edge recovery, structural stability, and interpretability.