Rademacher and Gaussian Complexities: Risk Bounds and Structural Results
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Localized Rademacher Complexities
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
On the size of convex hulls of small sets
The Journal of Machine Learning Research
Mathematical Modelling of Generalization
WIRN VIETRI 2002 Proceedings of the 13th Italian Workshop on Neural Nets-Revised Papers
Generalization Error Bounds for Threshold Decision Lists
The Journal of Machine Learning Research
Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets
Discrete Applied Mathematics
Aspects of discrete mathematics and probability in the theory of machine learning
Discrete Applied Mathematics
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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.