Deep Ensembles Meets Quantile Regression: Uncertainty-aware Imputation for Time Series

Real-world time series data frequently have significant amounts of missing values, posing challenges for advanced analysis. A common approach to address 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 could brings a potentially overlooked risk to the reliability of the intelligent system. Diffusion methods are proficient in estimating probability distributions but face challenges with high missing rates and moreover, computationally expensive due to the nature of the generative model framework. In this paper, we propose Quantile Sub-Ensembles, a novel method to estimate uncertainty with ensemble of quantile-regression-based task networks and then incorporate Quantile Sub-Ensembles into a non-generative time series imputation method. Our method not only produces accurate imputations that is robust to high missing rates, but also is computationally efficient due to the fast training of its non-generative model. We examine the performance of the proposed method on two real-world datasets, the air quality and health-care datasets, and conduct extensive experiments to show that our method outperforms other most of the baseline methods in making deterministic and probabilistic imputations. Compared with the diffusion method, CSDI, our approach can obtain comparable forecasting results which is better when more data is missing, and moreover consumes a much smaller computation overhead, yielding much faster training and test.