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Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF)
Trefor Evans · Prasanth B Nair

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #81

We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in O(p) time. Our GRIEF kernel consists of p eigenfunctions found using a Nyström approximation from a dense Cartesian product grid of inducing points. By exploiting algebraic properties of Kronecker and Khatri-Rao tensor products, computational complexity of the training procedure can be practically independent of the number of inducing points. This allows us to use arbitrarily many inducing points to achieve a globally accurate kernel approximation, even in high-dimensional problems. The fast likelihood evaluation enables type-I or II Bayesian inference on large-scale datasets. We benchmark our algorithms on real-world problems with up to two-million training points and 10^33 inducing points.

Author Information

Trefor Evans (University of Toronto)
Prasanth B Nair (University of Toronto)

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