Inference with Deep Gaussian Process State Space Models

In this paper, we address the problem of sequential processing of observations modeled by deep Gaussian process state space models. First, we introduce the model where the Gaussian processes are based on random features and where both the transition and observation functions of the models are unknown. Then we propose a method that can estimate the unknowns of the model. The method allows for incremental learning of the system without requiring all the historical information. We also propose an ensemble version of the method, where each member of the ensemble has its own set of features. We show with computer simulations that the method can track the latent states up to scale and rotation.