Likelihood-Free Inference in State-Space Models with Unknown Dynamics

We introduce a method for inferring and predicting latent states in the important and difficult case of state-space models where observations can only be simulated, and transition dynamics are unknown. In this setting, the likelihood of observations is not available and only synthetic observations can be generated from a black-box simulator. We propose a way of doing likelihood-free inference (LFI) of states and state prediction with a limited number of simulations. Our approach uses a multi-output Gaussian process for state inference, and a Bayesian Neural Network as a model of the transition dynamics for state prediction. We improve upon existing LFI methods for the inference task, while also accurately learning transition dynamics. The proposed method is necessary for modelling inverse problems in dynamical systems with computationally expensive simulations, as demonstrated in experiments with non-stationary user models.