Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition
This work addresses scalability issues in GP models for researchers and practitioners, though it builds incrementally on existing methods like stochastic variational inference and kernel interpolation.
The authors tackled the problem of scaling Gaussian Process (GP) models to billions of inducing inputs by proposing TT-GP, which uses Tensor Train decomposition for variational parameters, achieving state-of-the-art results on benchmarks like MNIST, CIFAR-10, and Airline.
We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure exploiting algebra. The key idea of our method is to use Tensor Train decomposition for variational parameters, which allows us to train GPs with billions of inducing inputs and achieve state-of-the-art results on several benchmarks. Further, our approach allows for training kernels based on deep neural networks without any modifications to the underlying GP model. A neural network learns a multidimensional embedding for the data, which is used by the GP to make the final prediction. We train GP and neural network parameters end-to-end without pretraining, through maximization of GP marginal likelihood. We show the efficiency of the proposed approach on several regression and classification benchmark datasets including MNIST, CIFAR-10, and Airline.