# Imputing Missing Events in Continuous-Time Event Streams

arXiv: https://arxiv.org/abs/1905.05570 · HTML: https://mlsanity.com/paper/1905.05570/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2019.

## Built on by (most cited first, 30 of 44)

- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [EasyTPP: Towards Open Benchmarking Temporal Point Processes](https://mlsanity.com/paper/2307.08097/) (2023)
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- [Learning Temporal Point Processes for Efficient Retrieval of Continuous Time Event Sequences](https://mlsanity.com/paper/2202.11485/) (2022)
- [HoTPP Benchmark: Are We Good at the Long Horizon Events Forecasting?](https://mlsanity.com/paper/2406.14341/) (2024)
- [Deep Continuous-Time State-Space Models for Marked Event Sequences](https://mlsanity.com/paper/2412.19634/) (2024)
- [Learning to Assimilate in Chaotic Dynamical Systems](https://mlsanity.com/paper/2111.01058/) (2021)
- [Interacting Diffusion Processes for Event Sequence Forecasting](https://mlsanity.com/paper/2310.17800/) (2023)
- [In-Context Learning of Temporal Point Processes with Foundation Inference Models](https://mlsanity.com/paper/2509.24762/) (2025)
- [EventFlow: Forecasting Temporal Point Processes with Flow Matching](https://mlsanity.com/paper/2410.07430/) (2024)
- [Detecting the Future: All-at-Once Event Sequence Forecasting with Horizon Matching](https://mlsanity.com/paper/2408.13131/) (2024)
- [Probabilistic Querying of Continuous-Time Event Sequences](https://mlsanity.com/paper/2211.08499/) (2022)
- [Modeling Continuous Time Sequences with Intermittent Observations using Marked Temporal Point Processes](https://mlsanity.com/paper/2206.12414/) (2022)
- [A Differentiable Partially Observable Generalized Linear Model with Forward-Backward Message Passing](https://mlsanity.com/paper/2402.01263/) (2024)
- [Self-supervised Adaptive Pre-training of Multilingual Speech Models for Language and Dialect Identification](https://mlsanity.com/paper/2312.07338/) (2023)
- [Probabilistic Modeling for Sequences of Sets in Continuous-Time](https://mlsanity.com/paper/2312.15045/) (2023)
- [ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes](https://mlsanity.com/paper/2504.20411/) (2025)
- [Retrieving Continuous Time Event Sequences using Neural Temporal Point Processes with Learnable Hashing](https://mlsanity.com/paper/2307.09613/) (2023)
- [Tapestry of Time and Actions: Modeling Human Activity Sequences using Temporal Point Process Flows](https://mlsanity.com/paper/2307.10305/) (2023)
- [Pretext Training Algorithms for Event Sequence Data](https://mlsanity.com/paper/2402.10392/) (2024)
- [Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes](https://mlsanity.com/paper/2511.01096/) (2025)
- [ReDiTT: Retrieval Augmented Conditional Diffusion Transformers for Asynchronous Time Series](https://mlsanity.com/paper/2607.12391/) (2026)
- [Signal Transformer: Complex-valued Attention and Meta-Learning for Signal Recognition](https://mlsanity.com/paper/2106.04392/) (2021)
- [Enhancing Asynchronous Time Series Forecasting with Contrastive Relational Inference](https://mlsanity.com/paper/2309.02868/) (2023)
- [Enhancing Multilingual Speech Recognition through Language Prompt Tuning and Frame-Level Language Adapter](https://mlsanity.com/paper/2309.09443/) (2023)
- [GMTR: Graph Matching Transformers](https://mlsanity.com/paper/2311.08141/) (2023)
- [DarkShot: Lighting Dark Images with Low-Compute and High-Quality](https://mlsanity.com/paper/2312.16805/) (2023)
- [TRLS: A Time Series Representation Learning Framework via Spectrogram for Medical Signal Processing](https://mlsanity.com/paper/2401.05431/) (2024)

## Abstract (arXiv)

Events in the world may be caused by other, unobserved events. We consider sequences of events in continuous time. Given a probability model of complete sequences, we propose particle smoothing---a form of sequential importance sampling---to impute the missing events in an incomplete sequence. We develop a trainable family of proposal distributions based on a type of bidirectional continuous-time LSTM: Bidirectionality lets the proposals condition on future observations, not just on the past as in particle filtering. Our method can sample an ensemble of possible complete sequences (particles), from which we form a single consensus prediction that has low Bayes risk under our chosen loss metric. We experiment in multiple synthetic and real domains, using different missingness mechanisms, and modeling the complete sequences in each domain with a neural Hawkes process (Mei & Eisner 2017). On held-out incomplete sequences, our method is effective at inferring the ground-truth unobserved events, with particle smoothing consistently improving upon particle filtering.