Reviews: Identification of Gaussian Process State Space Models

The authors derive a variational objective for inference and hyperparameter learning in a GPSSM. The authors apply a mean field variational approximation to the distribution over inducing points and a Gaussian approximation with Markov structure to the distribution over the sequence of latent states. The parameters of the latter depend on a bi-RNN. The variational bound is optimised using doubly stochastic gradient optimisation. The authors apply their algorithm to three simulated data examples, showing that particular applications may require the ability to flexibly choose kernel functions and that the algorithm recovers meaningful structure in the latent states.