The covering number in learning theory
Journal of Complexity
Regularized Principal Manifolds
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
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
Learning Relatively Small Classes
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Geometric Parameters of Kernel Machines
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
On different facets of regularization theory
Neural Computation
A tutorial on support vector regression
Statistics and Computing
Support Vector Machine Soft Margin Classifiers: Error Analysis
The Journal of Machine Learning Research
Kernel Matched Subspace Detectors for Hyperspectral Target Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning Bounds for Kernel Regression Using Effective Data Dimensionality
Neural Computation
Estimating the Support of a High-Dimensional Distribution
Neural Computation
Statistical properties of kernel principal component analysis
Machine Learning
The performance bounds of learning machines based on exponentially strongly mixing sequences
Computers & Mathematics with Applications
Nonparametric Quantile Estimation
The Journal of Machine Learning Research
Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets
Discrete Applied Mathematics
The covering number for some Mercer kernel Hilbert spaces
Journal of Complexity
Aggregation of SVM Classifiers Using Sobolev Spaces
The Journal of Machine Learning Research
On Relevant Dimensions in Kernel Feature Spaces
The Journal of Machine Learning Research
Oracle inequalities for support vector machines that are based on random entropy numbers
Journal of Complexity
A framework for kernel-based multi-category classification
Journal of Artificial Intelligence Research
Review: Using support vector machines in diagnoses of urological dysfunctions
Expert Systems with Applications: An International Journal
Classification Using Geometric Level Sets
The Journal of Machine Learning Research
Logistic classification with varying Gaussians
Computers & Mathematics with Applications
Covering numbers of Gaussian reproducing kernel Hilbert spaces
Journal of Complexity
The consistency analysis of coefficient regularized classification with convex loss
WSEAS Transactions on Mathematics
Predicting seminal quality with artificial intelligence methods
Expert Systems with Applications: An International Journal
On the convergence rate of lp-norm multiple kernel learning
The Journal of Machine Learning Research
Using robust dispersion estimation in support vector machines
Pattern Recognition
| Hi-index | 754.84 |
We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use of a viewpoint that is apparently novel in the field of statistical learning theory. The hypothesis class is described in terms of a linear operator mapping from a possibly infinite-dimensional unit ball in feature space into a finite-dimensional space. The covering numbers of the class are then determined via the entropy numbers of the operator. These numbers, which characterize the degree of compactness of the operator can be bounded in terms of the eigenvalues of an integral operator induced by the kernel function used by the machine. As a consequence, we are able to theoretically explain the effect of the choice of kernel function on the generalization performance of support vector machines