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On consistency and robustness properties of Support Vector Machines for heavy-tailed distributions

(2009) STATISTICS AND ITS INTERFACE. 2(3). p.311-327
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Abstract
Support Vector Machines (SVMs) are known to be consistent and robust for classification and regression if they are based on a Lipschitz continuous loss function and on a bounded kernel with a dense and separable reproducing kernel Hilbert space. These facts are even true in the regression context for unbounded output spaces, if the target function f is integrable with respect to the marginal distribution of the input variable X and if the output variable Y has a finite first absolute moment. The latter assumption clearly excludes distributions with heavy tails, e. g., several stable distributions or some extreme value distributions which occur in financial or insurance projects. The main point of this paper is that we can enlarge the applicability of SVMs even to heavy-tailed distributions, which violate this moment condition. Results on existence, uniqueness, representation, consistency, and statistical robustness are given.
Keywords
REGRESSION, CONVEX RISK MINIMIZATION

Citation

Please use this url to cite or link to this publication:

MLA
Christmann, Andreas, Arnout Van Messem, and Ingo Steinwart. “On Consistency and Robustness Properties of Support Vector Machines for Heavy-tailed Distributions.” STATISTICS AND ITS INTERFACE 2.3 (2009): 311–327. Print.
APA
Christmann, A., Van Messem, A., & Steinwart, I. (2009). On consistency and robustness properties of Support Vector Machines for heavy-tailed distributions. STATISTICS AND ITS INTERFACE, 2(3), 311–327.
Chicago author-date
Christmann, Andreas, Arnout Van Messem, and Ingo Steinwart. 2009. “On Consistency and Robustness Properties of Support Vector Machines for Heavy-tailed Distributions.” Statistics and Its Interface 2 (3): 311–327.
Chicago author-date (all authors)
Christmann, Andreas, Arnout Van Messem, and Ingo Steinwart. 2009. “On Consistency and Robustness Properties of Support Vector Machines for Heavy-tailed Distributions.” Statistics and Its Interface 2 (3): 311–327.
Vancouver
1.
Christmann A, Van Messem A, Steinwart I. On consistency and robustness properties of Support Vector Machines for heavy-tailed distributions. STATISTICS AND ITS INTERFACE. 2009;2(3):311–27.
IEEE
[1]
A. Christmann, A. Van Messem, and I. Steinwart, “On consistency and robustness properties of Support Vector Machines for heavy-tailed distributions,” STATISTICS AND ITS INTERFACE, vol. 2, no. 3, pp. 311–327, 2009.
@article{3120502,
  abstract     = {Support Vector Machines (SVMs) are known to be consistent and robust for classification and regression if they are based on a Lipschitz continuous loss function and on a bounded kernel with a dense and separable reproducing kernel Hilbert space. These facts are even true in the regression context for unbounded output spaces, if the target function f is integrable with respect to the marginal distribution of the input variable X and if the output variable Y has a finite first absolute moment. The latter assumption clearly excludes distributions with heavy tails, e. g., several stable distributions or some extreme value distributions which occur in financial or insurance projects. The main point of this paper is that we can enlarge the applicability of SVMs even to heavy-tailed distributions, which violate this moment condition. Results on existence, uniqueness, representation, consistency, and statistical robustness are given.},
  author       = {Christmann, Andreas and Van Messem, Arnout and Steinwart, Ingo},
  issn         = {1938-7989},
  journal      = {STATISTICS AND ITS INTERFACE},
  keywords     = {REGRESSION,CONVEX RISK MINIMIZATION},
  language     = {eng},
  number       = {3},
  pages        = {311--327},
  title        = {On consistency and robustness properties of Support Vector Machines for heavy-tailed distributions},
  volume       = {2},
  year         = {2009},
}

Web of Science
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