# Probabilistic Modeling for Sequences of Sets in Continuous-Time

arXiv: https://arxiv.org/abs/2312.15045 · HTML: https://mlsanity.com/paper/2312.15045/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [HYPRO: A Hybridly Normalized Probabilistic Model for Long-Horizon Prediction of Event Sequences](https://mlsanity.com/paper/2210.01753/) (2022)
- [Imputing Missing Events in Continuous-Time Event Streams](https://mlsanity.com/paper/1905.05570/) (2019)
- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity](https://mlsanity.com/paper/2205.04107/) (2022)
- [Probabilistic Querying of Continuous-Time Event Sequences](https://mlsanity.com/paper/2211.08499/) (2022)

## Built on by (most cited first, 2 of 2)

- [Deep Continuous-Time State-Space Models for Marked Event Sequences](https://mlsanity.com/paper/2412.19634/) (2024)
- [Model-Based Reinforcement Learning for Heterogeneous Multi-Robot Task Assignment Under Distribution Shifts](https://mlsanity.com/paper/2608.21554/) (2026)

## Abstract (arXiv)

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.