Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

TL;DR

This paper introduces a fully Bayesian method for inference and learning in nonlinear Gaussian process state-space models, utilizing Particle MCMC to efficiently estimate states and system dynamics.

Contribution

It develops a novel Bayesian framework that marginalizes over transition functions and employs Particle MCMC for scalable inference in nonparametric models.

Findings

Effective state estimation and system identification demonstrated

Model captures complex dynamical phenomena accurately

Sparse Gaussian processes reduce computational costs

Abstract

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.