  Gaussian process state-space models (GP-SSMs) are a very flexible family of
models of nonlinear dynamical systems. They comprise a Bayesian nonparametric
representation of the dynamics of the system and additional (hyper-)parameters
governing the properties of this nonparametric representation. The Bayesian
formalism enables systematic reasoning about the uncertainty in the system
dynamics. We present an approach to maximum likelihood identification of the
parameters in GP-SSMs, while retaining the full nonparametric description of
the dynamics. The method is based on a stochastic approximation version of the
EM algorithm that employs recent developments in particle Markov chain Monte
Carlo for efficient identification.
