Machine Learning
A data-dependent skeleton estimate for learning
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
A framework for structural risk minimisation
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
Scale-sensitive dimensions, uniform convergence, and learnability
Journal of the ACM (JACM)
Entropy Numbers, Operators and Support Vector Kernels
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
Efficient distribution-free learning of probabilistic concepts
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
IEEE Transactions on Information Theory
Structural risk minimization over data-dependent hierarchies
IEEE Transactions on Information Theory
Margin Distribution Bounds on Generalization
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Entropy Numbers, Operators and Support Vector Kernels
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Data-Dependent Margin-Based Generalization Bounds for Classification
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
On the doubt about margin explanation of boosting
Artificial Intelligence
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It is known that the covering numbers of a function class on a double sample (length 2m) can be used to bound the generalization performance of a classifier by using a margin based analysis. In this paper we show that one can utilize an analogous argument in terms of the observed covering numbers on a single m-sample (being the actual observed data points). The significance of this is that for certain interesting classes of functions, such as support vector machines, there are new techniques which allow one to find good estimates for such covering numbers in terms of the speed of decay of the eigenvalues of a Gram matrix. These covering numbers can be much less than a priori bounds indicate in situations where the particular data received is "easy". The work can be considered an extension of previous results which provided generalization performance bounds in terms of the VC-dimension of the class of hypotheses restricted to the sample, with the considerable advantage that the covering numbers can be readily computed, and they often are small.