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We propose a method (TT-GP) for approximate inference in Gaussian Process(GP) models. We build on previous scalable GP research including stochasticvariational inference based on inducing inputs, kernel interpolation, andstructure exploiting algebra. The key idea of our method is to use Tensor Traindecomposition for variational parameters, which allows us to train GPs withbillions of inducing inputs and achieve state-of-the-art results on severalbenchmarks. Further, our approach allows for training kernels based on deepneural networks without any modifications to the underlying GP model. A neuralnetwork learns a multidimensional embedding for the data, which is used by theGP to make the final prediction. We train GP and neural network parametersend-to-end without pretraining, through maximization of GP marginal likelihood.We show the efficiency of the proposed approach on several regression andclassification benchmark datasets including MNIST, CIFAR-10, and Airline.

Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition