Deep sub-ensembles meets quantile regression: uncertainty-aware imputation for time series

Real-world time series data often exhibits substantial missing values, posing challenges for advanced analysis. A common approach to addressing this issue is imputation, where the primary challenge lies in determining the appropriate values to fill in. While previous deep learning methods have proven effective for time series imputation, they often produce overconfident imputations, which poses a potentially overlooked risk to the reliability of the intelligent system. Diffusion methods are proficient in estimating probability distributions but face challenges under a high missing rate and are, moreover, computationally expensive due to the nature of the generative model framework. In this paper, we propose Quantile Sub-Ensembles, a novel method that estimates uncertainty with ensembles of quantile-regression-based task networks and incorporate Quantile Sub-Ensembles into a non-generative time series imputation method. Our method not only produces accurate and reliable imputations, but also remains computationally efficient due to its non-generative framework. We conduct extensive experiments on five real-world datasets, and the results demonstrates superior performance in both deterministic and probabilistic imputation compared to baselines across most experimental settings. The code is available at https://github.com/yingliu-coder/QSE.