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Likelihood-free inference (LFI) has been successfully applied to state-spacemodels, where the likelihood of observations is not available but syntheticobservations generated by a black-box simulator can be used for inferenceinstead. However, much of the research up to now have been restricted to cases,in which a model of state transition dynamics can be formulated in advance andthe simulation budget is unrestricted. These methods fail to address theproblem of state inference when simulations are computationally expensive andthe Markovian state transition dynamics are undefined. The approach proposed inthis manuscript enables LFI of states with a limited number of simulations byestimating the transition dynamics, and using state predictions as proposalsfor simulations. In the experiments with non-stationary user models, theproposed method demonstrates significant improvement in accuracy for both stateinference and prediction, where a multi-output Gaussian process is used for LFIof states, and a Bayesian Neural Network as a surrogate model of transitiondynamics.

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