To improve the forecasting capabilities, we extend this classical model by conditionally linear state-to-switch dynamics, while leaving the partial tractability of the conditional Gaussian linear part intact. Furthermore, we use an auxiliary variable approach with a decoder-type neural network that allows for more complex non-linear emission models and multivariate observations. We propose a Monte Carlo objective that leverages the conditional linearity by computing the corresponding conditional expectations in closed-form and a suitable proposal distribution that is factorised similarly to the optimal proposal distribution. We evaluate our approach on several popular time series forecasting datasets as well as image streams of simulated physical systems. Our results show improved forecasting performance compared to other deep state-space model approaches.

Strengths: Soundness: The model formulation appears to be mathematically sound. As with several previous works, the authors utilize linear-Gaussian distributions for dynamics, which have the benefit of permitting exact computation of expectations, e.g. The authors propose two main improvements over related models: 1) the use of recurrent switch transitions through Gaussian switch variables, and 2) non-linear emission models through the use of an additional (auxiliary) latent variable, z. They train this model with a sequential Monte Carlo objective utilized in previous works. This paper builds off of many of the theoretical developments of previous works, adding a couple of useful techniques.

This paper proposes an extension to state-switching Gaussian linear systems, which extends the ideas of traditional Kalman filtering to the setting of switching states.

To improve the forecasting capabilities, we extend this classical model by conditionally linear state-to-switch dynamics, while leaving the partial tractability of the conditional Gaussian linear part intact. Furthermore, we use an auxiliary variable approach with a decoder-type neural network that allows for more complex non-linear emission models and multivariate observations. We propose a Monte Carlo objective that leverages the conditional linearity by computing the corresponding conditional expectations in closed-form and a suitable proposal distribution that is factorised similarly to the optimal proposal distribution. We evaluate our approach on several popular time series forecasting datasets as well as image streams of simulated physical systems. Our results show improved forecasting performance compared to other deep state-space model approaches.