Local Rademacher complexities

Details Local Rademacher complexities Local Rademacher complexities

2005-08-16

arxiv.org/abs/math/0508275v1

Annals of Statistics 2005, Vol. 33, No. 4, 1497-1537

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000282 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000282

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.

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