Latent-driven Imputation and Forecasting for partially observed Time Series (LIFTS)

Abstract

Partially observed multivariate time series pose two coupled challenges: recovering missing measurements and forecasting future trajectories when observation patterns are informative. Existing methods often assume ignorable missingness or use the mask only as an auxiliary input. We propose LIFTS (Latent-driven Imputation and Forecasting for partly observed Time Series), a probabilistic framework in which a latent process jointly governs the complete measurement trajectory and observation mask, allowing observation patterns to inform latent-state inference for both forecasting and imputation. LIFTS combines flexible neural-network parameterizations with a forward-backward architecture: the forward pass performs filtering and autoregressive forecasting, while the backward pass performs smoothing and conditional multiple imputation. The model and inference components are trained jointly using a masked energy score and self-masking. We establish forward-backward distributional representations for the general framework and, for an explicit structural subclass, provide full-law identification and consistency guarantees. Simulations and an application to PhysioNet 2019 show that LIFTS provides accurate point predictions, improved distributional accuracy, and well-calibrated predictive intervals; it outperforms competing methods particularly when training data are limited and has substantially faster inference than the diffusion-based baseline.

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BibTeX RIS

BibTeX

@misc{wu2026latentdriven,
  title = {{Latent-driven Imputation and Forecasting for partially observed Time Series (LIFTS)}},
  author = {Sanyou Wu and Ying Wei and Kaizheng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03916},
  eprint = {2610.03916},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03916},
}

RIS

TY  - UNPB
TI  - Latent-driven Imputation and Forecasting for partially observed Time Series (LIFTS)
AU  - Sanyou Wu
AU  - Ying Wei
AU  - Kaizheng Wang
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.03916
UR  - https://arxiv.org/abs/2610.03916
AB  - Partially observed multivariate time series pose two coupled challenges: recovering missing measurements and forecasting future trajectories when observation patterns are informative. Existing methods often assume ignorable missingness or use the mask only as an auxiliary input. We propose LIFTS (Latent-driven Imputation and Forecasting for partly observed Time Series), a probabilistic framework in which a latent process jointly governs the complete measurement trajectory and observation mask, allowing observation patterns to inform latent-state inference for both forecasting and imputation. LIFTS combines flexible neural-network parameterizations with a forward-backward architecture: the forward pass performs filtering and autoregressive forecasting, while the backward pass performs smoothing and conditional multiple imputation. The model and inference components are trained jointly using a masked energy score and self-masking. We establish forward-backward distributional representations for the general framework and, for an explicit structural subclass, provide full-law identification and consistency guarantees. Simulations and an application to PhysioNet 2019 show that LIFTS provides accurate point predictions, improved distributional accuracy, and well-calibrated predictive intervals; it outperforms competing methods particularly when training data are limited and has substantially faster inference than the diffusion-based baseline.
ER  -

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