Sharing Temporal Structure for Joint Time-Mark Prediction

Distinct event types can exhibit different timing profiles without requiring separate temporal components. We introduce Shared Temporal Mixture (STMix), a history-conditioned joint time-mark model that uses shared temporal structure for both learning and probability queries. Each mixture component pairs a temporal density with a categorical mark distribution, allowing each type to combine the same temporal components with different weights. During joint likelihood training, observed times and marks determine component responsibilities, enabling events of different types to shape common temporal patterns. Tractable component cumulative distributions express marked next-event window probabilities and forecasts after an event-free wait as finite sums without numerical time integration. A query algorithm prepares components once per observed history and reuses endpoint evaluations across types, horizons, and requests. Experiments on four real-world datasets demonstrate competitive joint prediction; matched structural comparisons on three datasets achieve better test likelihood with 69–86% fewer total parameters than type-specific models. Query experiments show competitive window forecasts, while endpoint reuse yields 1.38–2.60x speedups over a vectorized implementation of the same model without caching.