Learning rates for regularized classifiers using multivariate polynomial kernels

Authors:
Hongzhi Tong;Di-Rong Chen;Lizhong Peng
Affiliations:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China and Department of Mathematics, University of International Business and Economics, Beijing 100029, PR China;Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, Beijing 100083, PR China;LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China
Venue:
Journal of Complexity
Year:
2008

Citing 13
Cited 4

A training algorithm for optimal margin classifiers

COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Bernstein-Durrmeyer polynomials on a simplex

Journal of Approximation Theory
Support-Vector Networks

Machine Learning
Least Squares Support Vector Machine Classifiers

Neural Processing Letters
An introduction to support Vector Machines: and other kernel-based learning methods

An introduction to support Vector Machines: and other kernel-based learning methods
Support Vector Machines and the Bayes Rule in Classification

Data Mining and Knowledge Discovery
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
Learning Rates of Least-Square Regularized Regression

Foundations of Computational Mathematics
Multi-kernel regularized classifiers

Journal of Complexity
Analysis of Support Vector Machines Regression

Foundations of Computational Mathematics
Fast rates for support vector machines

COLT'05 Proceedings of the 18th annual conference on Learning Theory
The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network

IEEE Transactions on Information Theory

The consistency analysis of coefficient regularized classification with convex loss

WSEAS Transactions on Mathematics
Learning Rates for Regularized Classifiers Using Trigonometric Polynomial Kernels

Neural Processing Letters
Finite rank kernels for multi-task learning

Advances in Computational Mathematics
Full length article: Approximation by multivariate Bernstein-Durrmeyer operators and learning rates of least-squares regularized regression with multivariate polynomial kernels

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

Regularized classifiers (a leading example is support vector machine) are known to be a kind of kernel-based classification methods generated from Tikhonov regularization schemes, and the polynomial kernels are the original and also probably the most important kernels used in them. In this paper, we provide an error analysis for the regularized classifiers using multivariate polynomial kernels. We introduce Bernstein-Durrmeyer polynomials, whose reproducing kernel Hilbert space norms and approximation properties in L^1 space play a key role in the analysis of regularization error. We also introduce the standard estimation of sample error, and derive explicit learning rates for these algorithms.