HGTHP: a novel hyperbolic geometric transformer hawkes process for event prediction.

Event sequences with spatiotemporal characteristics have been rapidly produced in various domains, such as earthquakes in seismology, electronic medical records in health care, and transactions in the financial market. These data are discrete events that are continuous and often continue for weeks, months, or years, and past events may trigger subsequent events. In this context, modeling spatiotemporal event sequences and forecasting the occurrence time and marker of the next event has become a hot topic. However, existing models either fail to capture the long-term temporal dependencies or ignore the essential spatial information between sequences. Moreover, existing models learn the influence of past events and predicted future events in Euclidean space, which has been shown to cause a significant distortion in hierarchical structure data. To correctly predict future events from historical events and design interventions and controls to guide the event dynamics to the desired results and inspired by the high capacity of modeling data in hyperbolic space, we proposed a novel hyperbolic graph transformer Hawkes process (HGTHP) model to capture the long-term temporal dependencies and spatial information from historical events with a hierarchical structure. The core concept of the HGTHP is to integrate the learned spatial information into the event embedding as auxiliary information and capture long-short term temporal dependencies from event sequences in non-Euclidean space by a hyperbolic self-attention mechanism. Numerous experiments on synthetic and real-world datasets proved that the proposed model obtains spatiotemporal information from hyperbolic space, and its predictions outperform those of state-of-the-art baselines in both time and marker, proving the proposed model's effectiveness. [ABSTRACT FROM AUTHOR]