From Prospective Actions to Events: Lifecycle Marked Temporal Point Processes

A Marked Temporal Point Process (MTPP) is a stochastic process that models the timing and types of events in continuous time. MTPPs are widely used to characterize asynchronous event sequences in domains such as mobility, e-commerce, and online behavior. In many applications, event histories also contain prospective actions, such as destination searches or cart additions, that point to possible future targets but may never be realized. While existing models can represent these actions as part of event history, how an action's predictive status evolves as subsequent observations arrive has been under-explored. In this regime, we propose a prospective-action lifecycle MTPP (PAL-MTPP) that represents each prospective action as an evolving target-linked lifecycle state. PAL-MTPP updates these states using both subsequent events and no-event observations while preserving uncertainty about action realization. For events with multiple targets, we further introduce pairwise target interactions to refine target-set probabilities beyond independent target predictions. Experiments on real-world mobility and e-commerce datasets show that lifecycle-aware action modeling improves future-event prediction, while pairwise interactions provide additional gains for multi-target prediction.