Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF)

Trefor W. Evans; Prasanth B. Nair

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arXiv · 1807.02125

Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF)

Trefor W. Evans·Prasanth B. Nair

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Abstract

We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in $\mathcal{O}(p)$ time. Our GRIEF kernel consists of $p$ eigenfunctions found using a Nystrom 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.

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BibTeX RIS

Trefor W. Evans, Prasanth B. Nair. 2018-07-05. Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF). https://arxiv.org/abs/1807.02125

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