Temporal Point Processes

Temporal point processes describe event sequences through an intensity that specifies how likely an event is at each moment, often conditioned on past events and their marks. Classical Hawkes and renewal models capture self-excitation or recurring-event patterns, while neural intensity models, Transformers, neural ODEs, splines, Gaussian processes, and diffusion or flow methods add flexibility for complex temporal and spatiotemporal data. These models support next-event prediction, sequence generation, latent-intensity and network recovery, and applications ranging from healthcare and business logs to online activity and markets; evaluation commonly uses likelihood, timing and type accuracy, calibration, and synthetic stress tests. A key tension is balancing expressive models and scalable inference with interpretability, calibrated uncertainty, and reliable generalization when event histories are sparse or patterns shift.