How Good are Low-Rank Approximations in Gaussian Process Regression?
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Publication:6385453
arXiv2112.06410MaRDI QIDQ6385453
Author name not available (Why is that?)
Publication date: 12 December 2021
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.
Has companion code repository: https://github.com/arespanos/gurantees_gpr
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