Complexities of convex combinations and bounding the generalization error in classification

Details Complexities of convex combinations and bounding the generalization error in classification Complexities of convex combinations and bounding the generalization error in classification

2004-05-18

arxiv.org/abs/math/0405356v2

Annals of Statistics 2005, Vol. 33, No. 4, 1455-1496

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009053605000000228 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000228

We introduce and study several measures of complexity of functions from the convex hull of a given base class. These complexity measures take into account the sparsity of the weights of a convex combination as well as certain clustering properties of the base functions involved in it. We prove new upper confidence bounds on the generalization error of ensemble (voting) classification algorithms that utilize the new complexity measures along with the empirical distributions of classification margins, providing a better explanation of generalization performance of large margin classification methods.

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