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August 2005 Complexities of convex combinations and bounding the generalization error in classification
Vladimir Koltchinskii, Dmitry Panchenko
Ann. Statist. 33(4): 1455-1496 (August 2005). DOI: 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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Vladimir Koltchinskii. Dmitry Panchenko. "Complexities of convex combinations and bounding the generalization error in classification." Ann. Statist. 33 (4) 1455 - 1496, August 2005.


Published: August 2005
First available in Project Euclid: 5 August 2005

zbMATH: 1080.62045
MathSciNet: MR2166553
Digital Object Identifier: 10.1214/009053605000000228

Primary: 62G05
Secondary: 60F15 , 62G20

Keywords: ‎classification‎ , convex combination , Convex hull , empirical margin distribution , empirical process , Generalization error , margin

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 4 • August 2005
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