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How Good are Low-Rank Approximations in Gaussian Process Regression?

Daskalakis, C; Dellaportas, P; Panos, A; (2022) How Good are Low-Rank Approximations in Gaussian Process Regression? In: Proceedings of 36th AAAI conference on Artificial intelligence. (In press). Green open access

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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.

Type: Proceedings paper
Title: How Good are Low-Rank Approximations in Gaussian Process Regression?
Event: 36th AAAI conference on Artificial intelligence
Open access status: An open access version is available from UCL Discovery
Publisher version: https://aaai.org/Conferences/AAAI-22/
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10140705
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