  Likelihood-free inference (LFI) has been successfully applied to state-space
models, where the likelihood of observations is not available but synthetic
observations generated by a black-box simulator can be used for inference
instead. 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 and
the simulation budget is unrestricted. These methods fail to address the
problem of state inference when simulations are computationally expensive and
the Markovian state transition dynamics are undefined. The approach proposed in
this manuscript enables LFI of states with a limited number of simulations by
estimating the transition dynamics, and using state predictions as proposals
for simulations. In the experiments with non-stationary user models, the
proposed method demonstrates significant improvement in accuracy for both state
inference and prediction, where a multi-output Gaussian process is used for LFI
of states, and a Bayesian Neural Network as a surrogate model of transition
dynamics.
