An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
The covering number in learning theory
Journal of Complexity
A theoretical characterization of linear SVM-based feature selection
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Support Vector Machine Soft Margin Classifiers: Error Analysis
The Journal of Machine Learning Research
Some Properties of Regularized Kernel Methods
The Journal of Machine Learning Research
Model Selection for Regularized Least-Squares Algorithm in Learning Theory
Foundations of Computational Mathematics
Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)
Multi-kernel regularized classifiers
Journal of Complexity
Learnability of Gaussians with Flexible Variances
The Journal of Machine Learning Research
Consistency of kernel-based quantile regression
Applied Stochastic Models in Business and Industry
Classification with Gaussians and Convex Loss
The Journal of Machine Learning Research
On complexity issues of online learning algorithms
IEEE Transactions on Information Theory
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In this paper we study conditional quantile regression by learning algorithms generated from Tikhonov regularization schemes associated with pinball loss and varying Gaussian kernels. Our main goal is to provide convergence rates for the algorithm and illustrate differences between the conditional quantile regression and the least square regression. Applying varying Gaussian kernels improves the approximation ability of the algorithm. Bounds for the sample error are achieved by using a projection operator, a variance-expectation bound derived from a condition on conditional distributions and a tight bound for the covering numbers involving the Gaussian kernels.