  In order to integrate uncertainty estimates into deep time-series modelling,
Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep
learning models, however, such approaches typically rely on approximate
inference techniques such as variational inference which makes learning more
complex and often less scalable due to approximation errors. We propose a new
deep approach to Kalman filtering which can be learned directly in an
end-to-end manner using backpropagation without additional approximations. Our
approach uses a high-dimensional factorized latent state representation for
which the Kalman updates simplify to scalar operations and thus avoids hard to
backpropagate, computationally heavy and potentially unstable matrix
inversions. Moreover, we use locally linear dynamic models to efficiently
propagate the latent state to the next time step. The resulting network
architecture, which we call Recurrent Kalman Network (RKN), can be used for any
time-series data, similar to a LSTM (Hochreiter & Schmidhuber, 1997) but uses
an explicit representation of uncertainty. As shown by our experiments, the RKN
obtains much more accurate uncertainty estimates than an LSTM or Gated
Recurrent Units (GRUs) (Cho et al., 2014) while also showing a slightly
improved prediction performance and outperforms various recent generative
models on an image imputation task.
