## Electronic Journal of Statistics

### Optimal regression rates for SVMs using Gaussian kernels

#### Abstract

Support vector machines (SVMs) using Gaussian kernels are one of the standard and state-of-the-art learning algorithms. In this work, we establish new oracle inequalities for such SVMs when applied to either least squares or conditional quantile regression. With the help of these oracle inequalities we then derive learning rates that are (essentially) minmax optimal under standard smoothness assumptions on the target function. We further utilize the oracle inequalities to show that these learning rates can be adaptively achieved by a simple data-dependent parameter selection method that splits the data set into a training and a validation set.

#### Article information

Source
Electron. J. Statist., Volume 7 (2013), 1-42.

Dates
First available in Project Euclid: 11 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1357913280

Digital Object Identifier
doi:10.1214/12-EJS760

Mathematical Reviews number (MathSciNet)
MR3020412

Zentralblatt MATH identifier
1337.62073

#### Citation

Eberts, Mona; Steinwart, Ingo. Optimal regression rates for SVMs using Gaussian kernels. Electron. J. Statist. 7 (2013), 1--42. doi:10.1214/12-EJS760. https://projecteuclid.org/euclid.ejs/1357913280

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