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Regression depth and support vector machine

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  • Christmann, Andreas

Abstract

The regression depth method (RDM) proposed by Rousseeuw and Hubert [RH99] plays an important role in the area of robust regression for a continuous response variable. Christmann and Rousseeuw [CR01] showed that RDM is also useful for the case of binary regression. Vapnik?s convex risk minimization principle [Vap98] has a dominating role in statistical machine learning theory. Important special cases are the support vector machine (SVM), [epsilon]-support vector regression and kernel logistic regression. In this paper connections between these methods from different disciplines are investigated for the case of pattern recognition. Some results concerning the robustness of the SVM and other kernel based methods are given.

Suggested Citation

  • Christmann, Andreas, 2004. "Regression depth and support vector machine," Technical Reports 2004,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200454
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    1. Rousseeuw, Peter J. & Christmann, Andreas, 2003. "Robustness against separation and outliers in logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 315-332, July.
    2. Struyf, Anja J. & Rousseeuw, Peter J., 1999. "Halfspace Depth and Regression Depth Characterize the Empirical Distribution," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 135-153, April.
    3. Andreas Christmann & Paul Fischer & Thorsten Joachims, 2002. "Comparison between various regression depth methods and the support vector machine to approximate the minimum number of misclassifications," Computational Statistics, Springer, vol. 17(2), pages 273-287, July.
    4. Christmann, Andreas & Rousseeuw, Peter J., 1999. "Measuring overlap in logistic regression," Technical Reports 1999,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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