## The Annals of Statistics

#### Abstract

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present some applications to classification and prediction with convex function classes, and with kernel classes in particular.

#### Article information

Source
Ann. Statist., Volume 33, Number 4 (2005), 1497-1537.

Dates
First available in Project Euclid: 5 August 2005

https://projecteuclid.org/euclid.aos/1123250221

Digital Object Identifier
doi:10.1214/009053605000000282

Mathematical Reviews number (MathSciNet)
MR2166554

Zentralblatt MATH identifier
1083.62034

#### Citation

Bartlett, Peter L.; Bousquet, Olivier; Mendelson, Shahar. Local Rademacher complexities. Ann. Statist. 33 (2005), no. 4, 1497--1537. doi:10.1214/009053605000000282. https://projecteuclid.org/euclid.aos/1123250221

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