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Multivariate time series are everywhere. Nevertheless, real-world time seriesdata often exhibit numerous missing values, which is the time series imputationtask. Although previous deep learning methods have been shown to be effectivefor time series imputation, they are shown to produce overconfidentimputations, which might be a potentially overlooked threat to the reliabilityof the intelligence system. Score-based diffusion method(i.e., CSDI) iseffective for the time series imputation task but computationally expensive dueto the nature of the generative diffusion model framework. In this paper, wepropose a non-generative time series imputation method that produces accurateimputations with inherent uncertainty and meanwhile is computationallyefficient. Specifically, we incorporate deep ensembles into quantile regressionwith a shared model backbone and a series of quantile discriminationfunctions.This framework combines the merits of accurate uncertainty estimationof deep ensembles and quantile regression and above all, the shared modelbackbone tremendously reduces most of the computation overhead of the multipleensembles. We examine the performance of the proposed method on two real-worlddatasets: air quality and health-care datasets and conduct extensiveexperiments to show that our method excels at making deterministic andprobabilistic predictions. Compared with the score-based diffusion method:CSDI, we can obtain comparable forecasting results and is better when more datais missing. Furthermore, as a non-generative model compared with CSDI, theproposed method consumes a much smaller computation overhead, yielding muchfaster training speed and fewer model parameters.

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