Some Local Measures of Complexity of Convex Hulls and Generalization Bounds

  • Olivier Bousquet
  • Vladimir Koltchinskii
  • Dmitriy Panchenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2375)


We investigate measures of complexity of function classes based on continuity moduli of Gaussian and Rademacher processes. For Gaussian processes, we obtain bounds on the continuity modulus on the convex hull of a function class in terms of the same quantity for the class itself. We also obtain new bounds on generalization error in terms of localized Rademacher complexities. This allows us to prove new results about generalization performance for convex hulls in terms of characteristics of the base class. As a byproduct, we obtain a simple proof of some of the known bounds on the entropy of convex hulls.


Convex Hull Function Class Local Measure Base Class Generalization Error 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Olivier Bousquet
    • 1
  • Vladimir Koltchinskii
    • 2
  • Dmitriy Panchenko
    • 2
  1. 1.Centre de Mathématiques AppliquéesEcole PolytechniquePalaiseauFrance
  2. 2.Department of Mathematics and StatisticsThe University of New MexicoAlbuquerqueUSA

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