Andreas Christmann
Professor for Stochastics (Head)  

Research    Publications Presentations
Short CV Projects Software
Teaching Editorial activities Statistical consulting
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RESEARCH TOPICS

  • Mathematical statistics and applications
  • Statistical machine learning theory
  • Support Vector Machines
  • Kernel methods
  • empirical risk minimization
  • Nonparametrical statistics
  • Computational statistics
  • Robust statistics
  • Actuarial statistics and finance
  • Data Mining
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PUBLICATIONS

A list with the most often cited publications is available from:
Books and some recent publications are listed below.

BOOKS

  • Support Vector Machines
    Steinwart, I., Christmann, A. (2008).
    Springer, New York.
         Link to Book Website

  • Data Mining und Statistik in Hochschulen und Wirtschaft. Proceedings der 6. Konferenz der SAS®-Anwender in Forschung und Entwicklung (KSFE).
    Eds.: Christmann, A., Weihs, C. (2003).
    Shaker-Verlag Aachen
    Link to Publisher Website

RECENT PUBLICATIONS

  • On the robustness of regularized pairwise learning methods based on kernels.
    Christmann, A. and Zhou, Ding-Xuan (2016).
    Journal of Complexity, 37, 1-33.
    Link to: Journal
    Preprint: PDF, arXiv

  • Learning rates for the risk of kernel based quantile regression estimators in additive models.
    Christmann, A. and Zhou, Ding-Xuan (2016).
    Analysis and Applications, 14(3), 449-477.
    Online: PDF,
    DOI: 10.1142/S0219530515500050
    Preprint: PDF, arXiv

  • A short note on extension theorems and their connection to universal consistency in machine learning.
    Christmann, A. , Dumpert, F. and Dao-Hong, Xiang (2016).
    Preprint: PDF, arXiv

  • Estimation of scale functions to model heteroscedasticity by regularised kernel-based quantile methods.
    Hable, R., Christmann, A. (2014).
    Journal of Nonparametric Statistics, 26(2), 219-239.
    Preprint: PDF, arXiv

  • On the Consistency of the Bootstrap Approach for Support Vector Machines and Related Kernel Based Methods.
    Christmann, A., Hable, R. (2013).
    Chapter 20 in: Empirical Inference. Festschrift in Honor of Vladimir N. Vapnik. Eds. B. Schökopf, Z. Luo, V. Vovk. Springer, New York.. pp. 231-244.
    Preprint: PDF, arXiv.

  • Qualitative Robustness of Bootstrap Approximations for Kernel Based Methods.
    Christmann, A., Salibian-Barrera, M., Van Aelst, S. (2013).
    Chapter 16 in "Robustness and Complex Data Structures. Festschrift in Honour of Ursula Gather", Eds. C. Becker, S. Kuhnt, R. Fried (2013), pp. 263-278.Springer, Heidelberg, New York.
    Preprint: PDF, arXiv

  • On the Bootstrap Approach for Support Vector Machines and Related Kernel Based Methods.
    Christmann, A., Hable, R. (2013).
    Proceedings 59th ISI World Statistics Congress, 25-30 August 2013, Hong Kong. pp. 3779-3784.
    click here.

  • Qualitative Robustness of Bootstrap Approximations for Kernel Based Methods.
    Christmann, M, Salibian-Barrera, S. Van Aelst (2013).
    Proceedings 59th ISI World Statistics Congress, 25-30 August 2013, Hong Kong. pp. 1802-1807.
    click here.

  • Robustness Versus Consistency in Ill-Posed Classification and Regression Problems.
    Hable, R., Christmann, A. (2013). pp. 27-35.
    In: A. Giusti, G. Ritter, M. Vichi (Eds.): Classification and Data Mining, Springer, Berlin.

  • Consistency of support vector machines using additive kernels for additive models.
    Christmann, A. and Hable, R. (2012).
    Computational Statistics and Data Analysis, 56, 854-873.
    Former preprint: PDF, arXiv

  • On qualitative robustness of support vector machines.
    Hable, R., Christmann, A. (2011).
    Journal of Multivariate Analysis, 102, 993-1007.
    PDF, arXiv

  • Estimating Conditional Quantiles with the Help of the Pinball Loss
    Steinwart, I., Christmann, A. (2011).
    Bernoulli, 17, 211-225.
    PDF, arXiv Link to Bernoulli Journal

  • Universal Kernels on Non-Standard Input Spaces.
    Christmann, A. and Steinwart, I., (2010).
    Advances in Neural Information Processing Systems, 23, 406-414.
    PDF

  • A Review on Consistency and Robustness Properties of Support Vector Machines for Heavy-Tailed Distributions.
    Van Messem, A. and Christmann, A. (2010).
    Advances in Data Analysis and Classification, 4, 199-220.

  • Robustness of Reweighted Least Squares Kernel Based Regression.
    Debruyne, M., Christmann, A., Hubert, M., Suykens, J.A.K. (2010).
    Journal of Multivariate Analysis, 101, 447-463.
    PDF (preprint)

  • On the interface of statistics and machine learning.
    Christmann, A., Shen, X., editors. (2009).
    Special issue: Statistics and Its Interface, 2 (3).
    Link to Journal Website

  • Fast Learning from Non-i.i.d. Observations.
    Steinwart, I., Christmann, A. (2009).
    Advances in Neural Information Processing Systems, 22, 1768-1776.
    PDF

  • On Consistency and Robustness Properties of Support Vector Machines for Heavy-Tailed Distributions
    Christmann, A., Van Messem, A., Steinwart, I. (2009).
    Statistics and Its Interface, 2, 311-327.
        PDF

  • Sparsity of SVMs that use the epsilon-insensitive loss
    Steinwart, I., Christmann, A. (2009).
    Advances in Neural Information Processing Systems, 21, pages 1569--1576, eds. D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou.
    PDF

  • How Support Vector Machines can estimate quantiles and the median.
    Steinwart, I., Christmann, A. (2008).
    Advances in Neural Information Processing Systems, 20, pages 305-312, eds. J.C. Platt, D. Koller, Y. Singer, and S. Roweis, MIT Press, Cambridge, MA.
    PDF

  • Bouligand derivatives and robustness of support vector machines for regression.
    Christmann, A. and Van Messem, A. (2008). Journal of Machine Learning Research, 9, 915-936.
        PDF  •  Link to Journal

  • Consistency of kernel based quantile regression.
    Christmann, A. and Steinwart, I. (2008).
    Applied Stochastic Models in Business and Industry (Wiley), 24(2), 171-183.
        PDF  •  Link to Journal

  • Consistency and robustness of kernel based regression.
    Christmann, A. and Steinwart, I. (2007).
    Bernoulli 13(3), 799-819.
         PDF  •  Link to Journal

  • Robust Learning From Bites for Data Mining.
    Christmann, A., Steinwart, I., and Hubert, M. (2007).
    Computational Statistics and Data Analysis, 52, 347-361.
        (available online at www.sciencedirect.com)
        PDF (Preprint)

  • A Robust Estimator for the Tail Index of Pareto-type Distributions.
    B. Vandewalle, J. Beirlant, A. Christmann, M. Hubert (2007).
    Computational Statistics and Data Analysis, 51, 6252-6268.
        (available online at www.sciencedirect.com)
        PDF (Preprint)

  • Robust estimation of Cronbach's alpha.
    Christmann, A. and Van Aelst, S. (2006).
    Journal of Multivariate Analysis, 97, 1660-1674.
        (available online at www.sciencedirect.com)
        PDF

  • Regression depth and support vector machine..
    Christmann, A. (2006). American Mathematical Society, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 72, 71-85.
        PDF (Preprint)

  • Angiographic Follow-Up After Carotid Artery Stenting of Bifurcation Stenosis..
    Hauth, E.A., Jansen, C., Drescher, R., Schwarz, M., Christmann, A., Jaeger, H., Forsting, M., Mathias, K. (2006).
    Fortschritte auf dem Gebiet der Röntgenstrahlen und der bildgebenden Verfahren, 178, 787-793.

  • Analysis of Surgical Management of Calvarial Tumours and First Results of a Newly Designed Robotic Trepanation System.
    M. Engelhardt, P. Bast, N. Jeblink, W. Lauer, A. Popovic, H. Eufinger, M. Scholz, A. Christmann, A. Harders, K. Radermacher, K. Schmieder (2006)
    Minimally Invasive Neurochirurgy, 49, 98-103.
        PDF

  • On a Strategy to Develop Robust and Simple Tariffs from Motor Vehicle Insurance Data.
    Andreas Christmann (2005).
    Acta Mathematicae Applicatae Sinica, English Series, 21, 193-208.
    Link to Journal: http://link.springer.com/article/10.1007/s10255-005-0229-8

  • Determination of hyper-parameters for kernel based classification and regression..
    Andreas Christmann, Karsten Lübke, Marcos Marin-Galiano, Stefan Rüping (2005).
    University of Dortmund, SFB-475, TR-38/2005.
        PDF

  • On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition.
    Andreas Christmann, Ingo Steinwart (2004).
    Journal of Machine Learning Research, 5, 1007-1034.
        PDF

  • An approach to model complex high-dimensional insurance data
    Andreas Christmann (2004).
    Allgemeines Statistisches Archiv, 88, 375-397.
        PDF

  • Insurance: an R-Program to Model Insurance Data..
    Andreas Christmann, Marcos Marin Galiano (2004).
    University of Dortmund, SFB-475, Technical Report.
        PDF

  • Robustness against separation and outliers in logistic regression.
    Peter J. Rousseeuw, Andreas Christmann (2003).
    Computational Statistics and Data Analysis, 43, 315-332.
        PDF

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RECENT PRESENTATIONS

  • Robust Pairwise Learning With Kernels.
    Oberwolfach workshop "Learning Theory and Approximation", Oberwolfach, Germany, July 3-9, 2016.
  • On Bootstrap and Robustness of Regularized Kernel Based Methods.
    4th IMS Asia Pacific Rim Meeting, The Chinese University of Hong Kong, June 27-30, 2016.
  • Regularized kernel methods with special emphasis on additive models.
    Symposium of Frontiers of Statistics and Data Sciences, The Hong Kong Polytechnic University, Hong Kong, June 25-26, 2016..
  • On consistency of regularized kernel methods.
    3rd Workshop on Mathematical Aspects of Data Science, Fudan University, Shanghai, May 20-23, 2016..
  • On Robustness Properties of Kernel Based Methods for Pairwise Learning
    12th German Probability and Statistics Days, Bochum, Germany, March 1-4, 2016.
  • On Robustness Properties of Kernel Based Methods for Pairwise Learning
    CMStatistics 2015, London, UK, December 12-14, 2015.
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SHORT CV

  • Dissertation and Habilitation at the University of Dortmund.
  • After positions as a visiting professor at the KU Leuven (Belgium) and as professor at universities in Dortmund and Brussels (Belgium) I am Full Professor and Chair for Stochastics at the University of Bayreuth since 2008.
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PROJECTS

  • Support vector machines for stochastically dependent data.
    (joint with: PD Dr. R. Hable)
    DFG.

SELECTED FINISHED PROJECTS

  • Construction of effective and fair insurance tariffs
    Cooperation partner: Verband öffentlicher Versicherer, Düsseldorf, Germany.
    Goals: Use methods from statistical machine learning and extreme value theory for the construction of insurance tariffs.
     
  • Risk differentiation in high-dimensional data structures.
    Project B7 in the Sonderforschungsbereich "Reduction of complexity for multivariate data structures" (SFB-475) at the Department of Statistics, University of Dortmund, Germany.
    Goals: Identification and modelling of complex dependency structures in high-dimensional and complex data sets.
     
  • Statistical software and algorithms
    DoMuS, University of Dortmund, Germany.
    Goals: Investigation of statistical properties of modern statistical methods, e.g. support vector machine and kernel logistic regression.
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SOFTWARE

R programs

    • insurance: an R-Program to Model insurance Data
      (M. Marin-Galiano, A. Christmann)
    • noverlap: n_overlap in binary regression models
    • ncomplete: n_complete in binary regression models
    noverlap, ncomplete, and an R-implementation of the S-PLUS code hlr for hidden logistic regression are available also from the CRAN-Mirrors.

  • S-Plus
    • hbdp: robust estimators with high breakdown points in generalized linear models
    • hlr: estimators MEL and WEMEL in the hidden logistic regression model
    • robust Cronbach's alpha: robust estimators of Cronbach's alpha (S-PLUS and SAS)
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    TEACHING

    Some Courses

    • Einführung in die Stochastik
    • Einführung in die Statistik
    • Support Vector Machines
    • Lineare Modelle
    • Seminare zu Stochastik / Mathematischer Statistik
    • Oberseminar
    • Mathematische Methoden für Wirtschaftswissenschaftler
    • Statistische Methoden I und II
    • Mathematical Statistics (Bachelor program, VUB, Brussels)
    • Generalized Linear Models (Master program, English, VUB and ULB, Brussels)
    • Mathematical Statistics 2 (Master program, English, ULB, Brussels).
    • New Developments in Mathematics (Bachelor program, VUB, Brussels).
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    EDITORIAL ACTIVITIES

    • Action Editor for Journal of Machine Learning Research (JMLR): since 2013
    • Associate Editor for Statistics and Its Interface: 2008-2010
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    STATISTICAL CONSULTING

    • I provide statistical consulting for employees of the University of Bayreuth as well as for external interested research institutions or companies and have more than 10 years of experience in statistical consulting. Statistical consulting can range from a single counselling interview to a joint project.
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    HOW TO REACH ME

    • To see a map of the city Bayreuth, you can click on the next link and type in the word Bayreuth. City map. The university campus is located in the south of Bayreuth.
    • Campus of the university as PDF file My office is in building NW II.
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    LINKS

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    Universität Bayreuth -