  Multivariate time series with missing values are common in areas such as
healthcare and finance, and have grown in number and complexity over the years.
This raises the question whether deep learning methodologies can outperform
classical data imputation methods in this domain. However, naive applications
of deep learning fall short in giving reliable confidence estimates and lack
interpretability. We propose a new deep sequential latent variable model for
dimensionality reduction and data imputation. Our modeling assumption is simple
and interpretable: the high dimensional time series has a lower-dimensional
representation which evolves smoothly in time according to a Gaussian process.
The non-linear dimensionality reduction in the presence of missing data is
achieved using a VAE approach with a novel structured variational
approximation. We demonstrate that our approach outperforms several classical
and deep learning-based data imputation methods on high-dimensional data from
the domains of computer vision and healthcare, while additionally improving the
smoothness of the imputations and providing interpretable uncertainty
estimates.
