Latent Matters: Learning Deep State-Space Models

Alexej Klushyn, Richard Kurle, Maximilian Soelch, Botond Cseke, Patrick van der Smagt

Keywords: variational inference, latent-variable models, state-space models, deep state-space models, Bayesian filtering and smoothing, empirical Bayes, constrained optimisation

TL;DR: In this paper, we address the question of how to learn deep state-space models in order to obtain accurate temporal predictions of observed dynamical systems.

Abstract: Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model actually learns the underlying dynamics. We therefore propose a constrained optimisation framework as a general approach for training DSSMs. Building upon this, we introduce the extended Kalman VAE (EKVAE), which combines amortised variational inference with classic Bayesian filtering/smoothing to model dynamics more accurately than RNN-based DSSMs. Our results show that the constrained optimisation framework significantly improves system identification and prediction accuracy on the example of established state-of-the-art DSSMs. The EKVAE outperforms previous models w.r.t. prediction accuracy, achieves remarkable results in identifying dynamical systems, and can furthermore successfully learn state-space representations where static and dynamic features are disentangled.

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