Covering numbers for support vector machines
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
The Informational Complexity of Learning: Perspectives on Neural Networks and Generative Grammar
The Informational Complexity of Learning: Perspectives on Neural Networks and Generative Grammar
IEEE Transactions on Information Theory
Are loss functions all the same?
Neural Computation
Support Vector Machine Soft Margin Classifiers: Error Analysis
The Journal of Machine Learning Research
SVM Soft Margin Classifiers: Linear Programming versus Quadratic Programming
Neural Computation
Mercer theorem for RKHS on noncompact sets
Journal of Complexity
Multi-kernel regularized classifiers
Journal of Complexity
Infinite-σ Limits For Tikhonov Regularization
The Journal of Machine Learning Research
Learnability of Gaussians with Flexible Variances
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
Derivative reproducing properties for kernel methods in learning theory
Journal of Computational and Applied Mathematics
Parzen windows for multi-class classification
Journal of Complexity
Learning with sample dependent hypothesis spaces
Computers & Mathematics with Applications
Oracle inequalities for support vector machines that are based on random entropy numbers
Journal of Complexity
Gradient learning in a classification setting by gradient descent
Journal of Approximation Theory
Hermite learning with gradient data
Journal of Computational and Applied Mathematics
Mercer theorem for RKHS on noncompact sets
Journal of Complexity
Semisupervised multicategory classification with imperfect model
IEEE Transactions on Neural Networks
Classification with Gaussians and Convex Loss
The Journal of Machine Learning Research
Online Learning with Samples Drawn from Non-identical Distributions
The Journal of Machine Learning Research
Multiclass support vector machines for adaptation in MIMO-OFDM wireless systems
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
The relationship between generalization error and the training sample number of SVM
ICNC'09 Proceedings of the 5th international conference on Natural computation
Rates of convergence of the functional k-nearest neighbor estimate
IEEE Transactions on Information Theory
Semi-supervised learning based on high density region estimation
Neural Networks
Estimating divergence functionals and the likelihood ratio by convex risk minimization
IEEE Transactions on Information Theory
Logistic classification with varying Gaussians
Computers & Mathematics with Applications
Covering numbers of Gaussian reproducing kernel Hilbert spaces
Journal of Complexity
Full length article: Concentration estimates for the moving least-square method in learning theory
Journal of Approximation Theory
Mercer’s theorem, feature maps, and smoothing
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Application of integral operator for regularized least-square regression
Mathematical and Computer Modelling: An International Journal
Classification with non-i.i.d. sampling
Mathematical and Computer Modelling: An International Journal
Conditional quantiles with varying Gaussians
Advances in Computational Mathematics
Learning theory approach to minimum error entropy criterion
The Journal of Machine Learning Research
Journal of Multivariate Analysis
Generalization ability of fractional polynomial models
Neural Networks
Conjugate relation between loss functions and uncertainty sets in classification problems
The Journal of Machine Learning Research
Generalization Bounds of Regularization Algorithm with Gaussian Kernels
Neural Processing Letters
Statistical analysis of the moving least-squares method with unbounded sampling
Information Sciences: an International Journal
| Hi-index | 0.12 |
The covering number of a ball of a reproducing kernel Hilbert space as a subset of the continuous function space plays an important role in Learning Theory. We give estimates for this covering number by means of the regularity of the Mercer kernel K. For convolution type kernels K(x, t) = k(x - t) on [0, 1]n, we provide estimates depending on the decay of k, the Fourier transform of k. In particular, when k decays exponentially, our estimate for this covering number is better than all the previous results and covers many important Mercer kernels. A counter example is presented to show that the eigenfunctions of the Hilbert-Schmidt operator LK associated with a Mercer kernel K may not be uniformly bounded. Hence some previous methods used for estimating the covering number in Learning Theory are not valid. We also provide an example of a Mercer kernel to show that LK½ may not be generated by a Mercer kernel.