Probabilistic Modeling for Sequences of Sets in Continuous-Time
This addresses a practical limitation in event sequence modeling for applications involving set-valued data, representing an incremental advancement by extending existing intensity-based models.
The paper tackles the problem of modeling sequences where each event is associated with a set of items in continuous-time, which existing neural marked temporal point processes cannot handle, and develops a framework with inference methods that achieve orders-of-magnitude efficiency improvements in probabilistic queries over direct sampling on real-world datasets.
Neural marked temporal point processes have been a valuable addition to the existing toolbox of statistical parametric models for continuous-time event data. These models are useful for sequences where each event is associated with a single item (a single type of event or a "mark") -- but such models are not suited for the practical situation where each event is associated with a set of items. In this work, we develop a general framework for modeling set-valued data in continuous-time, compatible with any intensity-based recurrent neural point process model. In addition, we develop inference methods that can use such models to answer probabilistic queries such as "the probability of item $A$ being observed before item $B$," conditioned on sequence history. Computing exact answers for such queries is generally intractable for neural models due to both the continuous-time nature of the problem setting and the combinatorially-large space of potential outcomes for each event. To address this, we develop a class of importance sampling methods for querying with set-based sequences and demonstrate orders-of-magnitude improvements in efficiency over direct sampling via systematic experiments with four real-world datasets. We also illustrate how to use this framework to perform model selection using likelihoods that do not involve one-step-ahead prediction.