Provably Reliable Large-Scale Sampling from Gaussian Processes

TL;DR

This paper introduces a scalable method for generating large synthetic datasets from Gaussian processes with high-probability guarantees of fidelity, enabling better evaluation of approximate GP models at scale.

Contribution

It presents a novel approach to efficiently generate large-scale GP samples with provable reliability, overcoming computational limitations of naive methods.

Findings

Achieves scalable data generation for large GP samples

Provides probabilistic guarantees of sample fidelity

Reduces computational complexity from cubic to more manageable levels

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. Na\"{i}vely doing so would cost \(\mathcal{O}(n^3)\) flops and \(\mathcal{O}(n^2)\) memory to generate a size \(n\) sample. We demonstrate how to scale such data generation to large \(n\) whilst still providing guarantees that, with high probability, the sample is indistinguishable from a sample from the desired GP.