Probabilistic Imputation for Time-series Classification with Missing
  Data
SeungHyun Kim Hyunsu Kim EungGu Yun Hwangrae Lee Jaehun Lee Juho Lee
Multivariate time series data for real-world applications typically contain a
significant amount of missing values. The dominant approach for classification
with such missing values is to impute them heuristically with specific values
(zero, mean, values of adjacent time-steps) or learnable parameters. However,
these simple strategies do not take the data generative process into account,
and more importantly, do not effectively capture the uncertainty in prediction
due to the multiple possibilities for the missing values. In this paper, we
propose a novel probabilistic framework for classification with multivariate
time series data with missing values. Our model consists of two parts; a deep
generative model for missing value imputation and a classifier. Extending the
existing deep generative models to better capture structures of time-series
data, our deep generative model part is trained to impute the missing values in
multiple plausible ways, effectively modeling the uncertainty of the
imputation. The classifier part takes the time series data along with the
imputed missing values and classifies signals, and is trained to capture the
predictive uncertainty due to the multiple possibilities of imputations.
Importantly, we show that na\"ively combining the generative model and the
classifier could result in trivial solutions where the generative model does
not produce meaningful imputations. To resolve this, we present a novel
regularization technique that can promote the model to produce useful
imputation values that help classification. Through extensive experiments on
real-world time series data with missing values, we demonstrate the
effectiveness of our method.