We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a full Gaussian process. Closed-form and distributed computations allow for efficient and massive parallelisation while keeping the memory consumption small. Given sufficient computing resources, our model can handle arbitrarily large data sets, without

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... sparse approximations. We provide strong experimental evidence that our model can be applied to large data sets of sizes far beyond millions. Hence, our model has the potential to lay the foundation for general large-scale Gaussian process research.