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Local optimisation of Nyström samples through stochastic gradient descent

Hutchings, Matthew and Gauthier, Bertrand ORCID: 2023. Local optimisation of Nyström samples through stochastic gradient descent. Presented at: The 8th International Online & Onsite Conference on Machine Learning, Optimization, and Data Science, Siena, Italy, September 18 – 22, 2022. Lecture Notes in Computer Science. (13810) Springer, pp. 123-140. 10.1007/978-3-031-25599-1_10

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We study a relaxed version of the column-sampling problem for the Nyström approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nyström samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surrogate for the classical criteria used to assess the Nyström approximation accuracy; in this setting, we discuss how Nyström samples can be efficiently optimised through stochastic gradient descent. We perform numerical experiments which demonstrate that the local minimisation of the radial SKD yields Nyström samples with improved Nyström approximation accuracy in terms of trace, Frobenius and spectral norms

Item Type: Conference or Workshop Item (Paper)
Date Type: Published Online
Status: Published
Schools: Mathematics
Publisher: Springer
Funders: EPSRC
Date of First Compliant Deposit: 16 November 2022
Date of Acceptance: 2 June 2022
Last Modified: 13 Jun 2023 16:23

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