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Optimal rates for spectral algorithms with least-squares regression over Hilbert spaces

Abstract : In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regression, principal component regression, and gradient methods. We prove optimal, high-probability convergence results in terms of variants of norms for the studied algorithms, considering a capacity assumption on the hypothesis space and a general source condition on the target function. Consequently, we obtain almost sure convergence results with optimal rates. Our results improve and generalize previous results, filling a theoretical gap for the non-attainable cases.
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https://hal.inria.fr/hal-01958890
Contributor : Alessandro Rudi <>
Submitted on : Wednesday, December 19, 2018 - 12:06:32 AM
Last modification on : Tuesday, May 4, 2021 - 2:06:02 PM
Long-term archiving on: : Wednesday, March 20, 2019 - 1:33:22 PM

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Junhong Lin, Alessandro Rudi, Lorenzo Rosasco, Volkan Cevher. Optimal rates for spectral algorithms with least-squares regression over Hilbert spaces. Applied and Computational Harmonic Analysis, Elsevier, 2018. ⟨hal-01958890⟩

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