Subsampling for supervised learning in reproducing kernel Hilbert spaces

Eyal Vayness; Maxime Sangnier

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arXiv · 2606.21260

Subsampling for supervised learning in reproducing kernel Hilbert spaces

Eyal Vayness·Maxime Sangnier

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Abstract

In the era of big data, subsampling became a common practice in statistical learning. By selecting a subgroup of individuals based on which the learner is trained, subsampling aims at reducing the computational cost and time of the estimation step, and ideally leads to a decrease of its energy consumption and carbon footprint. This work focuses on a nonparametric setting, in which the hypotheses set lies in a reproducing kernel Hilbert space, and the estimator is a minimizer of an empirical risk reweighted \`a la Horvitz-Thompson. By studying the asymptotic properties of this estimator, we reveal an optimal subsampling scheme (regarding the trace of the covariance operator) and show that it can be used via plug-in. A numerical study on synthetic and real-world datasets shows the practicability and the benefit of the proposed approach.

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Eyal Vayness, Maxime Sangnier. 2026-06-19. Subsampling for supervised learning in reproducing kernel Hilbert spaces. https://arxiv.org/abs/2606.21260

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