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.

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:

- Arxiv overview paper on causality for machine learning, recommended by Judea Pearl
- 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. CIFAR news article.
- 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 assume 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 section two of this 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

- Short biosketch, Long CV: PDF, short German CV: PDF.
- 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 (since 2001)
- awards won by his lab
- J. K. Aggarwal Prize of the International Association for Pattern Recognition (2006)
- Max Planck Research Award (with Sebastian Thrun, 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)
- BBVA Foundation Frontiers of Knowledge Award (with Isabelle Guyon and Vladimir Vapnik, 2020)
- 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)
- Top computer scientists
- 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

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**.

755 results
(View BibTeX file of all listed publications)

**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)

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)

**Prior knowledge in support vector kernels**
In *Advances in Neural Information Processing Systems 10*, pages: 640-646 , (Editors: M Jordan and M Kearns and S Solla ), MIT Press, Cambridge, MA, USA, Eleventh Annual Conference on Neural Information Processing (NIPS), June 1998 (inproceedings)

**From regularization operators to support vector kernels**
In *Advances in Neural Information Processing Systems 10*, pages: 343-349, (Editors: M Jordan and M Kearns and S Solla), MIT Press, Cambridge, MA, USA, 11th Annual Conference on Neural Information Processing (NIPS), June 1998 (inproceedings)

**Übersicht durch Übersehen**
*Frankfurter Allgemeine Zeitung , Wissenschaftsbeilage*, March 1998 (misc)

**Learning view graphs for robot navigation**
*Autonomous Robots*, 5(1):111-125, March 1998 (article)

**Fast approximation of support vector kernel expansions, and an interpretation of clustering as approximation in feature spaces.**
In *Mustererkennung 1998*, pages: 125-132, Informatik aktuell, (Editors: P Levi and M Schanz and R-J Ahlers and F May), Springer, Berlin, Germany, 20th DAGM-Symposium, 1998 (inproceedings)

**Generalization bounds and learning rates for Regularized principal manifolds**
NeuroCOLT, 1998, NeuroColt2-TR 1998-027 (techreport)

**Kernel PCA pattern reconstruction via approximate pre-images.**
In *8th International Conference on Artificial Neural Networks*, pages: 147-152, Perspectives in Neural Computing, (Editors: L Niklasson and M Boden and T Ziemke), Springer, Berlin, Germany, 8th International Conference on Artificial Neural Networks, 1998 (inproceedings)

**Generalization Bounds for Convex Combinations of Kernel Functions**
Royal Holloway College, 1998 (techreport)

**Generalization Performance of Regularization Networks and Support Vector Machines via Entropy
Numbers of Compact Operators**
(19), NeuroCOLT, 1998, Accepted for publication in IEEE Transactions on Information Theory (techreport)

**Quantization Functionals and Regularized PrincipalManifolds**
NeuroCOLT, 1998, NC2-TR-1998-028 (techreport)

**Support Vector methods in learning and feature extraction**
*Ninth Australian Conference on Neural Networks*, pages: 72-78, (Editors: T. Downs, M. Frean and M. Gallagher), 1998 (talk)

**Convex Cost Functions for Support Vector Regression**
In *8th International Conference on Artificial Neural Networks*, pages: 99-104, Perspectives in Neural Computing, (Editors: L Niklasson and M Boden and T Ziemke), Springer, Berlin, Germany, 8th International Conference on Artificial Neural Networks, 1998 (inproceedings)

**Support-Vektor-Lernen**
In *Ausgezeichnete Informatikdissertationen 1997*, pages: 135-150, (Editors: G Hotz and H Fiedler and P Gorny and W Grass and S Hölldobler and IO Kerner and R Reischuk), Teubner Verlag, Stuttgart, 1998 (inbook)

**Support vector regression with automatic accuracy control.**
In *ICANN'98*, pages: 111-116, Perspectives in Neural Computing, (Editors: L Niklasson and M Boden and T Ziemke), Springer, Berlin, Germany, International Conference on Artificial Neural Networks (ICANN'98), 1998 (inproceedings)

**General cost functions for support vector regression.**
In *Ninth Australian Conference on Neural Networks*, pages: 79-83, (Editors: T Downs and M Frean and M Gallagher), 9th Australian Conference on Neural Networks (ACNN'98), 1998 (inproceedings)

**Asymptotically optimal choice of varepsilon-loss for support vector machines.**
In *8th International Conference on Artificial Neural Networks*, pages: 105-110, Perspectives in Neural Computing, (Editors: L Niklasson and M Boden and T Ziemke), Springer, Berlin, Germany, 8th International Conference on Artificial Neural Networks, 1998 (inproceedings)

**Support Vector Machine Reference Manual**
(CSD-TR-98-03), Department of Computer Science, Royal Holloway, University of London, 1998 (techreport)

**Comparing support vector machines with Gaussian kernels to radial basis function classifiers **
*IEEE Transactions on Signal Processing*, 45(11):2758-2765, November 1997 (article)

**The view-graph approach to visual navigation and spatial memory**
In *Artificial Neural Networks: ICANN ’97*, pages: 751-756, (Editors: W Gerstner and A Germond and M Hasler and J-D Nicoud), Springer, Berlin, Germany, 7th International Conference on Artificial Neural Networks, October 1997 (inproceedings)

**Predicting time series with support vector machines **
In *Artificial Neural Networks: ICANN’97*, pages: 999-1004, (Editors: Schölkopf, B. , C.J.C. Burges, A.J. Smola), Springer, Berlin, Germany, 7th International Conference on Artificial Neural Networks , October 1997 (inproceedings)

**Predicting time series with support vectur machines**
In *Artificial neural networks: ICANN ’97*, pages: 999-1004, (Editors: W Gerstner and A Germond and M Hasler and J-D Nicoud), Springer, Berlin, Germany, 7th International Conference on Artificial Neural Networks , October 1997 (inproceedings)

**Kernel principal component analysis**
In *Artificial neural networks: ICANN ’97, LNCS, vol. 1327*, pages: 583-588, (Editors: W Gerstner and A Germond and M Hasler and J-D Nicoud), Springer, Berlin, Germany, 7th International Conference on Artificial Neural Networks, October 1997 (inproceedings)

**Homing by parameterized scene matching**
In *Proceedings of the 4th European Conference on Artificial Life, (Eds.) P. Husbands, I. Harvey. MIT Press, Cambridge 1997*, pages: 236-245, (Editors: P Husbands and I Harvey), MIT Press, Cambridge, MA, USA, 4th European Conference on Artificial Life (ECAL97), July 1997 (inproceedings)

**Das Spiel mit dem künstlichen Leben.**
*Frankfurter Allgemeine Zeitung, Wissenschaftsbeilage*, June 1997 (misc)

**Improving the accuracy and speed of support vector learning machines**
In *Advances in Neural Information Processing Systems 9*, pages: 375-381, (Editors: M Mozer and MJ Jordan and T Petsche), MIT Press, Cambridge, MA, USA, Tenth Annual Conference on Neural Information Processing Systems (NIPS), May 1997 (inproceedings)

**Homing by parameterized scene matching**
(46), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, Febuary 1997 (techreport)

**Learning view graphs for robot navigation**
In *Proceedings of the 1st Intl. Conf. on Autonomous Agents*, pages: 138-147, (Editors: Johnson, W.L.), ACM Press, New York, NY, USA, First International Conference on Autonomous Agents (AGENTS '97), Febuary 1997 (inproceedings)

**Support vector learning**
pages: 173, Oldenbourg, München, Germany, 1997, Zugl.: Berlin, Techn. Univ., Diss., 1997 (book)

**Nonlinear Component Analysis as a Kernel Eigenvalue Problem**
(44), Max Planck Institute for Biological Cybernetics Tübingen, December 1996, This technical report has also been published elsewhere (techreport)

**Comparison of view-based object recognition algorithms using realistic 3D models**
In *Artificial Neural Networks: ICANN 96, LNCS, vol. 1112*, pages: 251-256, Lecture Notes in Computer Science, (Editors: C von der Malsburg and W von Seelen and JC Vorbrüggen and B Sendhoff), Springer, Berlin, Germany, 6th International Conference on Artificial Neural Networks, July 1996 (inproceedings)

**Learning View Graphs for Robot Navigation**
(33), Max Planck Institute for Biological Cybernetics, Tübingen,, July 1996 (techreport)

**Incorporating invariances in support vector learning machines**
In *Artificial Neural Networks: ICANN 96, LNCS vol. 1112*, pages: 47-52, (Editors: C von der Malsburg and W von Seelen and JC Vorbrüggen and B Sendhoff), Springer, Berlin, Germany, 6th International Conference on Artificial Neural Networks, July 1996, volume 1112 of Lecture Notes in Computer Science
(inproceedings)

**Künstliches Lernen**
In *Komplexe adaptive Systeme, Forum für Interdisziplinäre Forschung*, 15, pages: 93-117, Forum für interdisziplinäre Forschung, (Editors: S Bornholdt and PH Feindt), Röll, Dettelbach, 1996 (inbook)

**Aktives Erwerben eines Ansichtsgraphen zur diskreten Repräsentation offener Umwelten.**
*Fortschritte der K{\"u}nstlichen Intelligenz*, pages: 138-147, (Editors: M. Thielscher and S.-E. Bornscheuer), 1996 (poster)

**View-based cognitive map learning by an autonomous robot**
In *Proceedings International Conference on Artificial Neural Networks, vol. 2*, pages: 381-386, (Editors: Fogelman-Soulié, F.), EC2, Paris, France, Conférence Internationale sur les Réseaux de Neurones Artificiels (ICANN '95), October 1995 (inproceedings)