Communications of the ACM
What size net gives valid generalization?
Neural Computation
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Neural Computation
A universal theorem on learning curves
Neural Networks
Statistical theory of learning curves under entropic loss criterion
Neural Computation
The nature of statistical learning theory
The nature of statistical learning theory
Advances in kernel methods: support vector learning
Advances in kernel methods: support vector learning
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
AI Game Programming Wisdom
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Advances in Large Margin Classifiers
Advances in Large Margin Classifiers
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
The Kernel-Adatron Algorithm: A Fast and Simple Learning Procedure for Support Vector Machines
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Geometry and learning curves of kernel methods with polynomial kernels
Systems and Computers in Japan
Generalization error analysis for polynomial kernel methods: algebraic geometrical approach
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
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The generalization properties of learning classifiers with a polynomial kernel function are examined. In kernel methods, input vectors are mapped into a high-dimensional feature space where the mapped vectors are linearly separated. It is well-known that a linear dichotomy has an average generalization error or a learning curve proportional to the dimension of the input space and inversely proportional to the number of given examples in the asymptotic limit. However, it does not hold in the case of kernel methods since the feature vectors lie on a submanifold in the feature space, called the input surface. In this letter, we discuss how the asymptotic average generalization error depends on the relationship between the input surface and the true separating hyperplane in the feature space where the essential dimension of the true separating polynomial, named the class, is important. We show its upper bounds in several cases and confirm these using computer simulations.