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

2026-10-02

AI Summary

This study addresses the coupled challenge of missing value recovery and trajectory prediction in partially observed multivariate time series by proposing LIFTS, a probabilistic framework that jointly models complete trajectories and observation masks via latent variable processes. By enabling informative observation patterns to guide latent state inference, LIFTS overcomes limitations of conventional approaches that either ignore missingness mechanisms or treat masks merely as auxiliary inputs. Methodologically, it constructs a unified architecture integrating forward filtering-prediction with backward smoothing-imputation, optimized through neural network parameterization, mask energy scoring, and self-masking strategies, accompanied by theoretical consistency guarantees. Experiments on simulated data and the PhysioNet 2019 benchmark demonstrate that LIFTS achieves accurate point predictions and well-calibrated predictive intervals. It outperforms existing methods in low-data regimes while offering significantly faster inference than diffusion-based baselines.

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.

Problem

• partially observed time series
• missing data imputation
• time series forecasting
• informative missingness
• multivariate time series

Innovation

• Partially observed time series
• Probabilistic framework
• Forward-backward architecture
• Latent-driven imputation
• Masked energy score