How Good are Low-Rank Approximations in Gaussian Process Regression?
Abstract
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we bound the Kullback-Leibler divergence between an exact GP and one resulting from one of the afore-described low-rank approximations to its kernel, as well as between their corresponding predictive densities, and we also bound the error between predictive mean vectors and between predictive covariance matrices computed using the exact versus using the approximate GP. We provide experiments on both simulated data and standard benchmarks to evaluate the effectiveness of our theoretical bounds.
Cite
@article{arxiv.2112.06410,
title = {How Good are Low-Rank Approximations in Gaussian Process Regression?},
author = {Constantinos Daskalakis and Petros Dellaportas and Aristeidis Panos},
journal= {arXiv preprint arXiv:2112.06410},
year = {2022}
}
Comments
The arxiv ID of the correct article is arXiv:2004.01584. This arXiv article is redundant and it is not needed anymore