IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200315.html
   My bibliography  Save this paper

On robustness properties of convex risk minimization methods for pattern recognition

Author

Listed:
  • Christmann, Andreas
  • Steinwart, Ingo

Abstract

The paper brings together methods from two disciplines: machine learning theory and robust statistics. Robustness properties of machine learning methods based on convex risk minimization are investigated for the problem of pattern recognition. Assumptions are given for the existence of the influence function of the classifiers and for bounds of the influence function. Kernel logistic regression, support vector machines, least squares and the AdaBoost loss function are treated as special cases. A sensitivity analysis of the support vector machine is given.

Suggested Citation

  • Christmann, Andreas & Steinwart, Ingo, 2003. "On robustness properties of convex risk minimization methods for pattern recognition," Technical Reports 2003,15, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200315
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/49356/1/369860896.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Christmann, Andreas & Rousseeuw, Peter J., 1999. "Measuring overlap in logistic regression," Technical Reports 1999,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christmann, Andreas, 2004. "On a strategy to develop robust and simple tariffs from motor vehicle insurance data," Technical Reports 2004,16, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christmann, Andreas, 2004. "Regression depth and support vector machine," Technical Reports 2004,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2017. "Multivariate and functional classification using depth and distance," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(3), pages 445-466, September.
    3. Christmann, Andreas, 2004. "On a strategy to develop robust and simple tariffs from motor vehicle insurance data," Technical Reports 2004,16, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    5. Stanislav Nagy, 2021. "Halfspace depth does not characterize probability distributions," Statistical Papers, Springer, vol. 62(3), pages 1135-1139, June.
    6. Gather, Ursula & Fried, Roland & Lanius, Vivian, 2005. "Robust detail-preserving signal extraction," Technical Reports 2005,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Yi He & John H. J. Einmahl, 2017. "Estimation of extreme depth-based quantile regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 449-461, March.
    8. Jonas Baillien & Irène Gijbels & Anneleen Verhasselt, 2023. "Flexible asymmetric multivariate distributions based on two-piece univariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 159-200, February.
    9. Fijorek, Kamil & Sokolowski, Andrzej, 2012. "Separation-Resistant and Bias-Reduced Logistic Regression: STATISTICA Macro," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(c02).
    10. Xiaohui Liu & Karl Mosler & Pavlo Mozharovskyi, 2017. "Fast computation of Tukey trimmed regions and median in dimension p > 2," Working Papers 2017-71, Center for Research in Economics and Statistics.
    11. Hassairi, Abdelhamid & Regaieg, Ons, 2008. "On the Tukey depth of a continuous probability distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2308-2313, October.
    12. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    13. Christmann, Andreas & Steinwart, Ingo & Hubert, Mia, 2006. "Robust Learning from Bites for Data Mining," Technical Reports 2006,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Petra Laketa & Stanislav Nagy, 2022. "Halfspace depth for general measures: the ray basis theorem and its consequences," Statistical Papers, Springer, vol. 63(3), pages 849-883, June.
    15. Kong, Linglong & Zuo, Yijun, 2010. "Smooth depth contours characterize the underlying distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2222-2226, October.
    16. Lanius, Vivian & Gather, Ursula, 2007. "Robust online signal extraction from multivariate time series," Technical Reports 2007,38, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    17. Koshevoy, Gleb A., 2002. "The Tukey Depth Characterizes the Atomic Measure," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 360-364, November.
    18. Wei, Bei & Lee, Stephen M.S., 2012. "Second-order accuracy of depth-based bootstrap confidence regions," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 112-123.
    19. 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.
    20. Gather, Ursula & Davies, P. Laurie, 2004. "Robust Statistics," Papers 2004,20, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb475:200315. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/isdorde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.