Kernel truncated randomized ridge regression: Optimal rates and low noise acceleration

Kwang Sung Jun, Ashok Cutkosky, Francesco Orabona

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our algorithm has faster finite-time and asymptotic rates on problems where the Bayes risk with respect to the square loss is small. We state our results using standard tools from the theory of least square regression in RKHSs, namely, the decay of the eigenvalues of the associated integral operator and the complexity of the optimal predictor measured through the integral operator.
Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
StatePublished - Jan 1 2019
Externally publishedYes

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