  Gaussian processes (GPs) are Bayesian nonparametric generative models that
provide interpretability of hyperparameters, admit closed-form expressions for
training and inference, and are able to accurately represent uncertainty. To
model general non-Gaussian data with complex correlation structure, GPs can be
paired with an expressive covariance kernel and then fed into a nonlinear
transformation (or warping). However, overparametrising the kernel and the
warping is known to, respectively, hinder gradient-based training and make the
predictions computationally expensive. We remedy this issue by (i) training the
model using derivative-free global-optimisation techniques so as to find
meaningful maxima of the model likelihood, and (ii) proposing a warping
function based on the celebrated Box-Cox transformation that requires minimal
numerical approximations---unlike existing warped GP models. We validate the
proposed approach by first showing that predictions can be computed
analytically, and then on a learning, reconstruction and forecasting experiment
using real-world datasets.
