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Gaussian processes (GPs) are Bayesian nonparametric generative models thatprovide interpretability of hyperparameters, admit closed-form expressions fortraining and inference, and are able to accurately represent uncertainty. Tomodel general non-Gaussian data with complex correlation structure, GPs can bepaired with an expressive covariance kernel and then fed into a nonlineartransformation (or warping). However, overparametrising the kernel and thewarping is known to, respectively, hinder gradient-based training and make thepredictions computationally expensive. We remedy this issue by (i) training themodel using derivative-free global-optimisation techniques so as to findmeaningful maxima of the model likelihood, and (ii) proposing a warpingfunction based on the celebrated Box-Cox transformation that requires minimalnumerical approximations---unlike existing warped GP models. We validate theproposed approach by first showing that predictions can be computedanalytically, and then on a learning, reconstruction and forecasting experimentusing real-world datasets.

Learning non-Gaussian Time Series using the Box-Cox Gaussian Process