New Generative Model Improves Temporal Point Process Analysis

Temporal Point Processes (TPPs) model sequences of events occurring over time, but current methods, including neural generative models, often optimize per-event objectives without a global sequence-level loss. This limits their ability to capture the overall distribution of event sequences, and evaluating variable-length sequences lacks robust distributional discrepancy measures. This paper proposes a unified pathwise framework to address these limitations. It introduces the interarrival embedding, a stable and injective transformation that converts discrete jump paths of TPPs into continuous paths of bounded variation. This allows the powerful mathematical tools of rough path signatures, which characterize path distributions, to be applied to event sequences. Building on this, the researchers developed sigTPP, the first signature-based generative model for TPPs, trained with a path-level loss on complete trajectories. They also derived three new distributional discrepancies for counting paths, offering mathematically sound tools for evaluating generative TPP models. Empirical results show sigTPP consistently achieves superior performance across synthetic and real-world datasets, outperforming baselines in a majority of metrics.