Image credit: Herlinde Koelbl
# Bernhard Schölkopf

Director

Office: N4.019

Max-Planck-Ring 4

72076 Tübingen

Germany

Max-Planck-Ring 4

72076 Tübingen

Germany

+49 7071 601 551

+49 7071 601 552

My scientific interests are in the field of machine learning and inference from empirical data. This is usually based on statistical regularities, however, I take a particular interest in causal structures that underlie statistical dependences (arxiv overview paper on causality for machine learning, recommended by Judea Pearl). I have worked on a number of different applications of machine learning - in our field, you get "to play in everyone's backyard." Most recently, I have been trying to play in the backyard of astronomers and photographers.

I am heading the Department of Empirical Inference; take a look at our last formal **Research Overview** and **Alumni List**.

Many of my papers (PDF publication list) can downloaded if you click on the tab "publications;" alternatively, from arxiv or from http://www.kernel-machines.org/. Some additional information:

- We have written a book about causality, published as an open access title at MIT Press (PDF, with Jonas Peters and Dominik Janzing).
- Exoplanets we have discovered; one of them (K2-18b) recently made the news as the first habitable zone exoplanet whose atmosphere contains water.
- Some of my photographs: HDR composite of the 2019 solar eclipse viewed from La Silla, including the moon lit by the earth, wide angle view, view of the Alps from the southern black forest, a rainbow in La Palma, a lunar eclipse in 2007, the Andromeda galaxy, the Milky Way on the Roque de los Muchachos, the North America Nebula, the constellation Orion with Barnard's loop, and finally a picture of a beautiful northern light, taken a few years ago from the plane, on the way home from a conference in Vancouver. I always try to get a window seat when flying home from the North American west coast, and have often seen northern lights. Looking at the night sky is a fascinating and humbling experience.
- Some chapters of our book Learning with Kernels.
- Review paper on kernel methods in the Annals of Statistics.
- Short high-level introduction on statistical learning theory (in German) that appeared in the 2004 Jahrbuch of the Max Planck Society.
- Obituary for Alexej Chervonenkis (NIPS 2014).
- I am a member of the LIGO scientific collaboration to detect gravitational waves
- With the growing interest in (how to make money with) big data, machine learning has significantly gained in popularity. We have published an article in the German newspaper
*FAZ*in January 2015, discussing some of the implications. Disclaimer: the newspaper added some text that appears above our names - this was not written or approved by us. - In March 2018, I published an article about the cybernetic revolution in the German newspaper
*SZ*. It starts by pointing out that the current revolution is about processing (generating, converting, industrializing) information in much the same way the first two industrial revolutions dealt with processing (generating, converting, industrializing) energy. I have occasionally put forward this thesis (but I'm sure I am not the only one who thinks of it this way), for instance during a NYU symposium on the future of AI in January 2016 (here are some notes written by Max Tegmark), and in some more detail in an arxiv paper. The article also provides recommendations on what Europe should do to keep up with the development. - A children's book
- I do not engage in military research, and I believe AI/ML should not be used for aggressive military purposes. Open letter against autonomous AI weapons / open letter against a military collaboration of KAIST, with positive outcome / IEEE Global Initiative on Ethics of Autonomous and Intelligent Systems
- My department and/or members of the department (incl. myself) receive funding from a number of sources including Max Planck, the DFG, the Alexander-von-Humboldt foundation, Amazon, Google, Bosch, Facebook, the BMBF (German Ministry of Science), the EU, the ETH Zürich, the Land Baden-Wuerttemberg, the Hector foundation, the Koerber foundation, CIFAR, and the Stanford Center on Philanthropy and Civil Society.
- Stellungnahme zur Eindämmung der COVID-19-Pandemie

Machine Learning Causal Inference Artificial Intelligence Computational Photography Statistics

- M.Sc. in mathematics and Lionel Cooper Memorial Prize, University of London (1992)
- Diplom in physics (Tübingen, 1994)
- doctorate in computer science from the Technical University Berlin (1997); thesis on Support Vector Learning (main advisor: V. Vapnik, AT&T Bell Labs) won the annual dissertation prize of the German Association for Computer Science (GI)
- scientific member of the Max Planck Society, 2001
- awards won by his lab
- J. K. Aggarwal Prize of the International Association for Pattern Recognition, 2006
- Max Planck Research Award, 2011
- Academy Prize of the Berlin-Brandenburg Academy of Sciences and Humanities, 2012
- Royal Society Milner Award, 2014
- Member of the German National Academy of Science (Leopoldina) (since 2017)
- Distinguished Amazon Scholar (since 2017)
- Fellow of the ACM (Association for Computing Machinery) (since 2018)
- Gottfried-Wilhelm-Leibniz-Preis of the German Science Foundation (2018)
- Koerber European Science Prize (2019)
- Honorarprofessor at the Technical University Berlin (computer science) and at the Eberhard-Karls University Tübingen (physics)
- PDF publication list as of February 2019
- "ISI highly cited" (added in 2010)
- the h Index for Computer Science
- Google Scholar page
- co-editor-in-chief of JMLR, an early open access journal and now the flagship journal of machine learning
- member of the boards of the NIPS foundation and of the International Machine Learning Society
- PC member (e.g., NIPS, COLT, ICML, UAI, DAGM, CVPR, Snowbird Learning Workshop) and co-chair of various conferences (COLT'03, DAGM'04, NIPS'05, NIPS'06 and the first two kernel workshops).
- co-founder of the Machine Learning Summer Schools
- two-page CV: PDF.

If you'd like to **contact** me, please consider these two notes:

*1. I recently became co-editor-in-chief of JMLR. I work for JMLR because I believe in its open access model, but it takes a lot of time. During my JMLR term, please don't convince me to do other journal or grant reviewing duties.*

*2. I am not very organized with my e-mail so if you want to apply for a position in my lab, please send your application only to Sekretariat-Schoelkopf@tuebingen.mpg.de. Note that we do not respond to non-personalized applications that look like they are being sent to a large number of places simultaneously.*

We are always happy to receive outstanding applications for **PhD positions **and **postdocs**.

740 results
(View BibTeX file of all listed publications)

**Bound on the Leave-One-Out Error for 2-Class Classification using nu-SVMs**
University of Cambridge, 2001, Updated May 2003 (literature review expanded) (techreport)

**Inference Principles and Model Selection**
(01301), Dagstuhl Seminar, 2001 (techreport)

**Kernel Machine Based Learning for Multi-View Face
Detection and Pose Estimation**
In *Proceedings Computer Vision, 2001, Vol. 2*, pages: 674-679, IEEE Computer Society, 8th International Conference on Computer Vision (ICCV), 2001 (inproceedings)

**Some kernels for structured data**
Biowulf Technologies, 2001 (techreport)

**Robust ensemble learning**
In *Advances in Large Margin Classifiers*, pages: 207-220, Neural Information Processing Series, (Editors: AJ Smola and PJ Bartlett and B Schölkopf and D. Schuurmans), MIT Press, Cambridge, MA, USA, October 2000 (inbook)

**Entropy numbers for convex combinations and MLPs**
In *Advances in Large Margin Classifiers*, pages: 369-387, Neural Information Processing Series, (Editors: AJ Smola and PL Bartlett and B Schölkopf and D Schuurmans), MIT Press, Cambridge, MA,, October 2000 (inbook)

**Advances in Large Margin Classifiers**
pages: 422, Neural Information Processing, MIT Press, Cambridge, MA, USA, October 2000 (book)

**Natural Regularization from Generative Models**
In *Advances in Large Margin Classifiers*, pages: 51-60, Neural Information Processing Series, (Editors: AJ Smola and PJ Bartlett and B Schölkopf and D Schuurmans), MIT Press, Cambridge, MA, USA, October 2000 (inbook)

**Engineering Support Vector Machine Kernels That Recognize Translation Initiation Sites**
*Bioinformatics*, 16(9):799-807, September 2000 (article)

**Support vector method for novelty detection**
In *Advances in Neural Information Processing Systems 12*, pages: 582-588, (Editors: SA Solla and TK Leen and K-R Müller), MIT Press, Cambridge, MA, USA, 13th Annual Neural Information Processing Systems Conference (NIPS), June 2000 (inproceedings)

**v-Arc: Ensemble Learning in the Presence of Outliers**
In *Advances in Neural Information Processing Systems 12*, pages: 561-567, (Editors: SA Solla and TK Leen and K-R Müller), MIT Press, Cambridge, MA, USA, 13th Annual Neural Information Processing Systems Conference (NIPS), June 2000 (inproceedings)

**Invariant feature extraction and classification in kernel spaces**
In *Advances in neural information processing systems 12*, pages: 526-532, (Editors: SA Solla and TK Leen and K-R Müller), MIT Press, Cambridge, MA, USA, 13th Annual Neural Information Processing Systems Conference (NIPS), June 2000 (inproceedings)

**The entropy regularization information criterion**
In *Advances in Neural Information Processing Systems 12*, pages: 342-348, (Editors: SA Solla and TK Leen and K-R Müller), MIT Press, Cambridge, MA, USA, 13th Annual Neural Information Processing Systems Conference (NIPS), June 2000 (inproceedings)

**New Support Vector Algorithms**
*Neural Computation*, 12(5):1207-1245, May 2000 (article)

**Statistical Learning and Kernel Methods**
In *CISM Courses and Lectures, International Centre for Mechanical Sciences Vol.431*, *CISM Courses and Lectures, International Centre for
Mechanical Sciences*, 431(23):3-24, (Editors: G Della Riccia and H-J Lenz and R Kruse), Springer, Vienna, Data Fusion and Perception, 2000 (inbook)

**Choosing nu in support vector regression with
different noise models — theory and experiments**
In *Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks, IJCNN 2000, Neural Computing: New Challenges and Perspectives for the New Millennium*, IEEE, International Joint Conference on Neural Networks, 2000 (inproceedings)

**An Introduction to Kernel-Based Learning Algorithms**
In *Handbook of Neural Network Signal Processing*, 4, (Editors: Yu Hen Hu and Jang-Neng Hwang), CRC Press, 2000 (inbook)

**Robust Ensemble Learning for Data Mining**
In *Fourth Pacific-Asia Conference on Knowledge Discovery and Data Mining*, 1805, pages: 341-341, Lecture Notes in Artificial Intelligence, (Editors: H. Terano), Fourth Pacific-Asia Conference on Knowledge Discovery and Data Mining, 2000 (inproceedings)

**Sparse greedy matrix approximation for machine learning.**
In *17th International Conference on Machine Learning, Stanford, 2000*, pages: 911-918, (Editors: P Langley), Morgan Kaufman, San Fransisco, CA, USA, 17th International Conference on Machine Learning (ICML), 2000 (inproceedings)

**The Kernel Trick for Distances**
(MSR-TR-2000-51), Microsoft Research, Redmond, WA, USA, 2000 (techreport)

**Entropy Numbers of Linear Function Classes.**
In *13th Annual Conference on Computational Learning Theory*, pages: 309-319, (Editors: N Cesa-Bianchi and S Goldman), Morgan Kaufman, San Fransisco, CA, USA, 13th Annual Conference on Computational Learning Theory (COLT), 2000 (inproceedings)

**Kernel method for percentile feature extraction**
(MSR-TR-2000-22), Microsoft Research, 2000 (techreport)

**Engineering Support Vector Machine Kernels That Recognize Translation Initiation Sites in DNA**
In *German Conference on Bioinformatics (GCB 1999)*, October 1999 (inproceedings)

**Lernen mit Kernen: Support-Vektor-Methoden zur Analyse hochdimensionaler Daten**
*Informatik - Forschung und Entwicklung*, 14(3):154-163, September 1999 (article)

**Input space versus feature space in kernel-based methods **
*IEEE Transactions On Neural Networks*, 10(5):1000-1017, September 1999 (article)

**Shrinking the tube: a new support vector regression algorithm**
In *Advances in Neural Information Processing Systems 11*, pages: 330-336 , (Editors: MS Kearns and SA Solla and DA Cohn), MIT Press, Cambridge, MA, USA, 12th Annual Conference on Neural Information Processing Systems (NIPS), June 1999 (inproceedings)

**Kernel PCA and De-noising in feature spaces**
In *Advances in Neural Information Processing Systems 11*, pages: 536-542 , (Editors: MS Kearns and SA Solla and DA Cohn), MIT Press, Cambridge, MA, USA, 12th Annual Conference on Neural Information Processing Systems (NIPS), June 1999 (inproceedings)

**Semiparametric support vector and linear programming machines**
In *Advances in Neural Information Processing Systems 11*, pages: 585-591 , (Editors: MS Kearns and SA Solla and DA Cohn), MIT Press, Cambridge, MA, USA, Twelfth Annual Conference on Neural Information Processing Systems (NIPS), June 1999 (inproceedings)

**Kernel principal component analysis.**
In *Advances in Kernel Methods—Support Vector Learning*, pages: 327-352, (Editors: B Schölkopf and CJC Burges and AJ Smola), MIT Press, Cambridge, MA, 1999 (inbook)

**Estimating the support of a high-dimensional distribution**
(MSR-TR-99-87), Microsoft Research, 1999 (techreport)

**Single-class Support Vector Machines**
*Dagstuhl-Seminar on Unsupervised Learning*, pages: 19-20, (Editors: J. Buhmann, W. Maass, H. Ritter and N. Tishby), 1999 (poster)

**Classification on proximity data with LP-machines**
In *Artificial Neural Networks, 1999. ICANN 99*, 470, pages: 304-309, Conference Publications , IEEE, 9th International Conference on Artificial Neural Networks, 1999 (inproceedings)

**Kernel-dependent support vector error bounds**
In *Artificial Neural Networks, 1999. ICANN 99*, 470, pages: 103-108 , Conference Publications , IEEE, 9th International Conference on Artificial Neural Networks, 1999 (inproceedings)

**Linear programs for automatic accuracy control in regression**
In *Artificial Neural Networks, 1999. ICANN 99*, 470, pages: 575-580 , Conference Publications , IEEE, 9th International Conference on Artificial Neural Networks, 1999 (inproceedings)

**Classifying LEP data with support vector algorithms.**
In *Artificial Intelligence in High Energy Nuclear Physics 99*, Artificial Intelligence in High Energy Nuclear Physics 99, 1999 (inproceedings)

**Generalization Bounds via Eigenvalues of the Gram matrix**
(99-035), NeuroCOLT, 1999 (techreport)

**Regularized principal manifolds.**
In *Lecture Notes in Artificial Intelligence, Vol. 1572*, 1572, pages: 214-229 , Lecture Notes in Artificial Intelligence, (Editors: P Fischer and H-U Simon), Springer, Berlin, Germany, Computational Learning Theory: 4th European Conference, 1999 (inproceedings)

**Entropy numbers, operators and support vector kernels.**
In *Lecture Notes in Artificial Intelligence, Vol. 1572*, 1572, pages: 285-299, Lecture Notes in Artificial Intelligence, (Editors: P Fischer and H-U Simon), Springer, Berlin, Germany, Computational Learning Theory: 4th European Conference, 1999 (inproceedings)

**Sparse kernel feature analysis**
(99-04), Data Mining Institute, 1999, 24th Annual Conference of Gesellschaft f{\"u}r Klassifikation, University of Passau (techreport)

**Advances in Kernel Methods - Support Vector Learning**
MIT Press, Cambridge, MA, 1999 (book)

**Fisher discriminant analysis with kernels**
In *Proceedings of the 1999 IEEE Signal Processing Society Workshop*, 9, pages: 41-48, (Editors: Y-H Hu and J Larsen and E Wilson and S Douglas), IEEE, Neural Networks for Signal Processing IX, 1999 (inproceedings)

**Entropy numbers, operators and support vector kernels.**
In *Advances in Kernel Methods - Support Vector Learning*, pages: 127-144, (Editors: B Schölkopf and CJC Burges and AJ Smola), MIT Press, Cambridge, MA, 1999 (inbook)

**Navigation mit Schnappschüssen**
In *Mustererkennung 1998*, pages: 421-428, (Editors: P Levi and R-J Ahlers and F May and M Schanz), Springer, Berlin, Germany, 20th DAGM-Symposium, October 1998 (inproceedings)

**Where did I take that snapshot? Scene-based homing by image matching**
*Biological Cybernetics*, 79(3):191-202, October 1998 (article)

**On a Kernel-Based Method for Pattern Recognition, Regression, Approximation, and Operator Inversion **
*Algorithmica*, 22(1-2):211-231, September 1998 (article)

ei
Schölkopf, B.
**The moon tilt illusion**
*Perception*, 27(10):1229-1232, August 1998 (article)

**SVMs — a practical consequence of learning theory**
*IEEE Intelligent Systems and their Applications*, 13(4):18-21, July 1998 (article)

**Nonlinear Component Analysis as a Kernel Eigenvalue Problem**
*Neural Computation*, 10(5):1299-1319, July 1998 (article)

**Support vector machines **
*IEEE Intelligent Systems and their Applications*, 13(4):18-28, July 1998 (article)

**The connection between regularization operators and support vector kernels.**
*Neural Networks*, 11(4):637-649, June 1998 (article)