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Learning Rates for l1‐Regularized Kernel Classifiers

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  • Hongzhi Tong
  • Di-Rong Chen
  • Fenghong Yang

Abstract

We consider a family of classification algorithms generated from a regularization kernel scheme associated with l1‐regularizer and convex loss function. Our main purpose is to provide an explicit convergence rate for the excess misclassification error of the produced classifiers. The error decomposition includes approximation error, hypothesis error, and sample error. We apply some novel techniques to estimate the hypothesis error and sample error. Learning rates are eventually derived under some assumptions on the kernel, the input space, the marginal distribution, and the approximation error.

Suggested Citation

  • Hongzhi Tong & Di-Rong Chen & Fenghong Yang, 2013. "Learning Rates for l1‐Regularized Kernel Classifiers," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:496282
    DOI: 10.1155/2013/496282
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    References listed on IDEAS

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    1. Bartlett, Peter L. & Jordan, Michael I. & McAuliffe, Jon D., 2006. "Convexity, Classification, and Risk Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 138-156, March.
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