Provably Reliable Large-Scale Sampling from Gaussian Processes

preprint2023arXivOpen access

Abstract

When comparing approximate Gaussian process (GP) models, it can be helpful to be able to generate data from any GP. If we are interested in how approximate methods perform at scale, we may wish to generate very large synthetic datasets to evaluate them. Naïvely doing so would cost O(n3)\mathcal{O}(n^3) flops and O(n2)\mathcal{O}(n^2) memory to generate a size nn sample. We demonstrate how to scale such data generation to large nn whilst still providing guarantees that, with high probability, the sample is indistinguishable from a sample from the desired GP.

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