Probabilistic Modeling for Sequences of Sets in Continuous-Time

• URL: http://arxiv.org/abs/2312.15045v3
• Date: Mon, 18 Mar 2024 21:13:26 GMT
• Title: Probabilistic Modeling for Sequences of Sets in Continuous-Time
• Authors: Yuxin Chang, Alex Boyd, Padhraic Smyth,
• Abstract summary: We develop a general framework for modeling set-valued data in continuous-time. We also develop inference methods that can use such models to answer probabilistic queries.
• Score: 14.423456635520084
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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