Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces

Philipp Becker, Harit Pandya, Gregor H.W. Gebhardt, Cheng Zhao, Gerhard Neumann

Abstract:

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. Yet, 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. While our locally linear modelling and factorization assumptions are in general not true for the original low-dimensional state space of the system, the network finds a high-dimensional latent space where these assumptions hold to perform efficient inference. This state representation is learned jointly with the transition and noise models. The resulting network architecture, which we call Recurrent Kalman Network (RKN), can be used for any time-series data, similar to a LSTM (Hochreiter and 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.

Keywords: state estimation, recurrent neural networks, Kalman Filter, deep learning

TL;DR: Kalman Filter based recurrent model for efficient state estimation, principled uncertainty handling and end to end learning of dynamic models in high dimensional spaces.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:1905.07357/code)