Variational inference and learning for non-linear state-space models with state-dependent observation noise

In many real world dynamical systems, the inherent noise levels are not constant but depend on the state. Such aspects are often ignored in modelling because they make inference significantly more complicated. In this paper we propose a variational inference and learning algorithm for a non-linear state-space model with state-dependent observation noise. The observation noise level of each sample depends on additional latent variables with a linear dependence on the latent state. The method yields significant improvements in predictive performance over regular nonlinear state-space model as well as direct autoregressive prediction using Gaussian processes in a simulated Lorenz system with state-dependent noise and in stock price prediction.