- Main topics: statistical machine learning and robust statistics
- Further topics: data science, Big Data, kernel methods, mathematical statistics and applications.
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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
- Bootstrap SGD: Algorithmic Stability and Robustness.
Christmann, A., and Lei, Y. (2025).
Analysis and Applications, 23 (5), 675-703. PDF
Preprint on arxiv: PDF
- Optimality of Robust Online Learning.
Guo, Zheng-Chu, Christmann, A., and Shi, Lei (2023).
Foundations of Computational Mathematics. DOI 10.1007/s10208-023-09616-9.
Link to Journal: PDF
Preprint on arxiv: PDF
- Total Stability of SVMs and Localized SVMs.
Köhler, H. and Christmann, A. (2022).
Journal of Machine Learning Research, 23, 1-41.
Link to Journal: PDF
Link to preprint, arXiv https://arxiv.org/abs/2101.12678
- On the robustness of kernel-based pairwise learning.
Gensler, P. and Christmann, A. (2022).
In: Artificial Intelligence, Big Data and Data Science in Statistics: Challenges and Solutions in Environmetrics, the Natural Sciences and Technology (Eds: A. Steland and K.-L. Tsui), pp. 111-153. Springer, Cham.
Link: PDF
- Universal Consistency and Robustness of Localized Support Vector Machines.
Dumpert, F. and Christmann, A. (2018).
Neurocomputing, 315, 96-106.
Link to Journal: PDF
- Total stability of kernel methods.
Christmann, A., Xiang, Daohong, and Zhou, Ding-Xuan (2018).
Neurocomputing, 289, 101-118.
Link to Journal: PDF
- 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.
Link to Journal PDF,
DOI: 10.1142/S0219530515500050
Preprint: PDF, arXiv
- On extension theorems and their connection to universal consistency in machine learning.
Christmann, A. , Dumpert, F. and Xiang, D.-H. (2016).
Analysis and Applications, 14(6), 795-808.
Link to Journal PDF,
DOI: 10.1142/S0219530516400029
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.
Link to Journal
- 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.
Link to Book .
- 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.
Link to Book
Preprint: 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.
Link to Journal
Link to Preprint, arXiv
- On qualitative robustness of support vector machines.
Hable, R., Christmann, A. (2011).
Journal of Multivariate Analysis, 102, 993-1007.
Link to Journal
PDF, arXiv
- Estimating Conditional Quantiles with the Help of the Pinball Loss
Steinwart, I., Christmann, A. (2011).
Bernoulli, 17, 211-225.
Link to Journal
PDF, arXiv
- Universal Kernels on Non-Standard Input Spaces.
Christmann, A. and Steinwart, I., (2010).
Advances in Neural Information Processing Systems, 23, 406-414.
Link
- 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.
Link to Journal
- 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
- Fast Learning from Non-i.i.d. Observations.
Steinwart, I., Christmann, A. (2009).
Advances in Neural Information Processing Systems, 22, 1768-1776.
Link
- 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.
Link to Journal
- 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.
Link
- 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.
Link
- 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.
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.
Link to Journal
- Consistency and robustness of kernel based regression.
Christmann, A. and Steinwart, I. (2007).
Bernoulli 13(3), 799-819.
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.
Link to Journal
- 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.
Link to Journal
- Robust estimation of Cronbach's alpha.
Christmann, A. and Van Aelst, S. (2006).
Journal of Multivariate Analysis, 97, 1660-1674.
Link to Journal
- 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.
Link To Book
- 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.
Link to Journal
- 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
- 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.
Link to Journal
- An approach to model complex high-dimensional insurance data
Andreas Christmann (2004).
Allgemeines Statistisches Archiv, 88, 375-397.
Link to Journal
- 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.
Link to Journal
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- On Algorithmic Stability of Bootstrap SGD.
Department of Mathematics, Zhejiang Normal University, Jinhua, China, May 22, 2025.
- On Algorithmic Stability of Bootstrap SGD.
Department of Mathematics, Baptist University of Hong Kong, Hong Kong, May 19, 2025.
- On Algorithmic Stability of Bootstrap SGD.
Sydney Workshop on Mathematics of Data Science, The University of Sydney, Australia, December 04-06, 2024.
- On aspects of localized learning.
School of Mathematical Sciences, Zhejiang Normal University, Jinhua, China. May 10-17, 2024.
- On aspects of localized learning.
School of Mathematics and Statistics, The University of Sydney, Australia. March 09-17, 2024.
- Total Stability of Localized Learning.
International Conference on Applied Mathematics. Hong Kong, City University of Hong Kong, 30 May - 3 June 2023.
- Qualitative robustness of divide-and-conquer methods for large data sets.
EcoSta 2022. Kyoto, Japan. June 4-6, 2022.
- On qualitative robustness of divide-and-conquer methods.
EcoSta 2021. Hong Kong. June 24-26, 2021.
- Robustness and Machine Learning.
Zhejiang Normal University, Jinhua, China. October 2019.
- Robustness and Machine Learning.
3rd Internat. Conference on Kernel-Based Methods and Applications, Xi'an Jiatong-Liverpool University, Suzhou, China. October 11-14, 2019.
- Robustness of Localized Learning.
EcoSta 2019. National Chung Hsing University, Taiwan. June 25-27, 2019.
- Robust Localized Learning.
3rd International Conference on Mathematics of Data Science. City University, Hong Kong. June 19-23, 2019.
- Robustness and Stability of Kernel-Based Machine Learning.
DAGStat 2019, LMU, Munich. March 18-22, 2019.
- Robustness and Stability of Kernel-Based Machine Learning.
14th Workshop on Stochastic Models, Statistics and their Application. University of Dresden. March 6-8, 2019.
- Kernel based methods in machine learning.
European conference on data analysis. Paderborn. June 4-6, 2018.
- Robustness and stability of kernel based learning.
2nd International Conference on Econometrics and Statistics. Hong Kong. June 19-21, 2018.
- On Qualitative Robustness of Statistical Machine Learning With Kernels.
Applied Inverse Problems. Hangzhou, China. May 29 -June 02, 2017.
- On the Stability of Kernel Based Pairwise Learning Methods with Respect to $(P,\lambda,k)$.
International Conference on Computational Harmonic Analysis. Fudan University, Shanghai, China. May, 24-28, 2017.
- Robust Pairwise Learning With Kernels.
University of Hamburg, Germany, November 11, 2016.
- Robust Pairwise Learning With Kernels.
University of British Columbia, Vancouver, Canada, August 05, 2016.
- 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.
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- Dissertation and Habilitation at the University of Dortmund.
- After positions as a visiting professor at KU Leuven (Belgium) and
as professor at universities in Dortmund (Germany) and Brussels (VUB, Belgium) I am serving as Full Professor
and Chair of "Stochastics and Machine Learning" at the University of Bayreuth since 2008.
- Job offers: Eindhoven University of Technology (The Netherlands), University of Siegen, Chair (Germany)
- Oberwolfach workshop "Learning Theory and Approximation", July 3-9, 2016;
joint organization with Steve Smale, Ding-Xuan Zhou, and Kurt Jetter.
- Action Editor of "Journal of Machine Learning Research" (JMLR), 2013 - 2019
- Member of the JMLR Editorial board of reviewers, since 2020
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- Localized Statistical Learning with Kernels.
(joint with: Prof. Dr. Steinwart, University of Stuttgart)
DFG.
- Support vector machines for stochastically dependent data.
(joint with: PD Dr. R. Hable)
DFG.
- A Conservative Likelihood Framework for Statistical Signal Processing with Nonlinear Models.
DAAD.
- 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 SFB-475 sponsored by DFG "Reduction of complexity for multivariate data structures" 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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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
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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Some Courses
- Introduction to Stochastics
- Introduction to Statistics
- Support Vector Machines
- Statistical Machine Learning Theory
- Probability Theory
- Generalized Linear Models and Multivariate Statistics
- Linear Models
- Seminars on Stochastics and Machine Learning
- Statistics for Computer Scientists
- Mathematical Principles for Economists
- Statistical Methods I and II (for non-mathematicians)
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- Member of the JMLR Editorial board of reviewers: since 2020
- Action Editor for Journal of Machine Learning Research (JMLR): 2013-2019
- Associate Editor for Statistics and Its Interface: 2008-2010
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- I have more than 15 years of experience in statistical consulting.
Statistical consulting can range from a single counselling interview to a joint project.
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