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

TL;DR

This paper introduces a likelihood-free inference method for state-space models with unknown dynamics, enabling accurate state inference with limited simulations by estimating transition dynamics using Gaussian processes and neural networks.

Contribution

It presents a novel approach that estimates transition dynamics to perform likelihood-free inference in complex, computationally expensive state-space models.

Findings

Significant improvement in state inference accuracy

Effective use of Gaussian processes for state estimation

Bayesian Neural Networks as surrogate models for dynamics

Abstract

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.