Recoverability-Aware Imputation with Conditional Bayes Risk Estimation for Multivariate Time Series

The problem of missing values in time series is usually framed as a prediction problem where, given the contextual information, the model predicts every missing value. Though conceptually correct this approach overlooks a crucial aspect: the missing regions may differ in how recoverable they are given the available information. In this paper, we propose a recoverability-aware perspective of time series imputation that takes into account not only what to impute but also the uncertainty in this imputation. In our framework, the unrecoverability of the missing region is quantified via the conditional Bayes risk of the corresponding mask-aware missing region through a Contextual UnRecoverability Estimator (CURE) that learns this quantity from incomplete sequences. We then use the standard Bayes-risk decomposition to combine CURE with an imputer-specific residual-risk correction for selective imputation. Our experiments on synthetic dynamical systems demonstrate that regions with same size can have different levels of oracle unrecoverability for different generating configurations, and the imputers' errors correlate highly with the normalized oracle risk. Across five real-world datasets, seven imputers, MCAR and MAR missingness, and point and block corruption, CURE achieves a mean error-ranking correlation of 0.372, which increases to 0.507 after incorporating the imputer-specific correction. Total-risk ranking reduces AURC on average by 58.7% relative to random selection, compared with 53.8% for the strong imputer–CURE disagreement baseline, and yields lower AURC than disagreement in 56.3% of matched evaluations. For 50% coverage, selective RMSE is reduced by 38.4–62.7% for all five datasets relative to full coverage. These results support recoverability as a measurable basis for identifying which imputations can be trusted.