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Abstract: This paper deals with the selection of the training dataset in kernel-based methods for function reconstruction, with a focus on kernel ridge regression. A functional analysis is performed which, in the absence of noise, links the optimal sampling distribution to the one minimizing the difference between the kernel matrix and its low-rank Nyström approximation. From this standpoint, a statistical passive sampling approach is derived which uses the leverage scores of the columns of the kernel matrix to design a sampling distribution that minimizes an upper bound of the risk function. The proposed approach constitutes a passive method, able to select the optimal subset of training samples using only information provided by the input set and the kernel, but without needing to know the values of the function to be approximated. Furthermore, the proposed approach is backed up by numerical tests on real datasets.
Fuente: Signal Processing, 2022, 199, 108603
Publisher: Elsevier
Publication date: 01/10/2022
No. of pages: 10
Publication type: Article
DOI: 10.1016/j.sigpro.2022.108603
ISSN: 0165-1684,1872-7557
Spanish project: PID2019-104958RB-C41
Publication Url: https://doi.org/10.1016/j.sigpro.2022.108603
Consult in UCrea Read publication
PEDRO JUAN GIMÉNEZ FEBRER
ALBA PAGES ZAMORA
LUIS IGNACIO SANTAMARIA CABALLERO
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