Deep Ensembles Meets Quantile Regression: Uncertainty-aware Imputation
  for Time Series
Ying Liu Peng Cui Wenbo Hu Richang Hong
Multivariate time series are everywhere. Nevertheless, real-world time series
data often exhibit numerous missing values, which is the time series imputation
task. Although previous deep learning methods have been shown to be effective
for time series imputation, they are shown to produce overconfident
imputations, which might be a potentially overlooked threat to the reliability
of the intelligence system. Score-based diffusion method(i.e., CSDI) is
effective for the time series imputation task but computationally expensive due
to the nature of the generative diffusion model framework. In this paper, we
propose a non-generative time series imputation method that produces accurate
imputations with inherent uncertainty and meanwhile is computationally
efficient. Specifically, we incorporate deep ensembles into quantile regression
with a shared model backbone and a series of quantile discrimination
functions.This framework combines the merits of accurate uncertainty estimation
of deep ensembles and quantile regression and above all, the shared model
backbone tremendously reduces most of the computation overhead of the multiple
ensembles. We examine the performance of the proposed method on two real-world
datasets: air quality and health-care datasets and conduct extensive
experiments to show that our method excels at making deterministic and
probabilistic predictions. Compared with the score-based diffusion method:
CSDI, we can obtain comparable forecasting results and is better when more data
is missing. Furthermore, as a non-generative model compared with CSDI, the
proposed method consumes a much smaller computation overhead, yielding much
faster training speed and fewer model parameters.