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Journal Articles Applied and Computational Harmonic Analysis Year : 2018

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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Dates and versions

hal-01958890 , version 1 (19-12-2018)

Identifiers

  • HAL Id : hal-01958890 , version 1

Cite

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, 2018. ⟨hal-01958890⟩
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