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15 results (View BibTeX file of all listed publications)

2002

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Kernel Dependency Estimation

Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V.

(98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)

Abstract
We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. Output kernels also make it possible to encode prior information and/or invariances in the loss function in an elegant way. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images.

PDF [BibTex]

2002

Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V. Kernel Dependency Estimation (98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)

PDF [BibTex]

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Global Geometry of SVM Classifiers

Zhou, D., Xiao, B., Zhou, H., Dai, R.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)

Abstract
We construct an geometry framework for any norm Support Vector Machine (SVM) classifiers. Within this framework, separating hyperplanes, dual descriptions and solutions of SVM classifiers are constructed by a purely geometric fashion. In contrast with the optimization theory used in SVM classifiers, we have no complicated computations any more. Each step in our theory is guided by elegant geometric intuitions.

PDF PostScript [BibTex]

Zhou, D., Xiao, B., Zhou, H., Dai, R. Global Geometry of SVM Classifiers Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)

PDF PostScript [BibTex]

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Computationally Efficient Face Detection

Romdhani, S., Torr, P., Schölkopf, B., Blake, A.

(MSR-TR-2002-69), Microsoft Research, June 2002 (techreport)

Web [BibTex]

Romdhani, S., Torr, P., Schölkopf, B., Blake, A. Computationally Efficient Face Detection (MSR-TR-2002-69), Microsoft Research, June 2002 (techreport)

Web [BibTex]

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Kernel-based nonlinear blind source separation

Harmeling, S., Ziehe, A., Kawanabe, M., Müller, K.

EU-Project BLISS, January 2002 (techreport)

GZIP [BibTex]

Harmeling, S., Ziehe, A., Kawanabe, M., Müller, K. Kernel-based nonlinear blind source separation EU-Project BLISS, January 2002 (techreport)

GZIP [BibTex]

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A compression approach to support vector model selection

von Luxburg, U., Bousquet, O., Schölkopf, B.

(101), Max Planck Institute for Biological Cybernetics, 2002, see more detailed JMLR version (techreport)

Abstract
In this paper we investigate connections between statistical learning theory and data compression on the basis of support vector machine (SVM) model selection. Inspired by several generalization bounds we construct ``compression coefficients'' for SVMs, which measure the amount by which the training labels can be compressed by some classification hypothesis. The main idea is to relate the coding precision of this hypothesis to the width of the margin of the SVM. The compression coefficients connect well known quantities such as the radius-margin ratio R^2/rho^2, the eigenvalues of the kernel matrix and the number of support vectors. To test whether they are useful in practice we ran model selection experiments on several real world datasets. As a result we found that compression coefficients can fairly accurately predict the parameters for which the test error is minimized.

[BibTex]

von Luxburg, U., Bousquet, O., Schölkopf, B. A compression approach to support vector model selection (101), Max Planck Institute for Biological Cybernetics, 2002, see more detailed JMLR version (techreport)

[BibTex]

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Feature Selection and Transduction for Prediction of Molecular Bioactivity for Drug Design

Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B.

Max Planck Institute for Biological Cybernetics / Biowulf Technologies, 2002 (techreport)

Web [BibTex]

Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B. Feature Selection and Transduction for Prediction of Molecular Bioactivity for Drug Design Max Planck Institute for Biological Cybernetics / Biowulf Technologies, 2002 (techreport)

Web [BibTex]

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Observations on the Nyström Method for Gaussian Process Prediction

Williams, C., Rasmussen, C., Schwaighofer, A., Tresp, V.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2002 (techreport)

Abstract
A number of methods for speeding up Gaussian Process (GP) prediction have been proposed, including the Nystr{\"o}m method of Williams and Seeger (2001). In this paper we focus on two issues (1) the relationship of the Nystr{\"o}m method to the Subset of Regressors method (Poggio and Girosi 1990; Luo and Wahba, 1997) and (2) understanding in what circumstances the Nystr{\"o}m approximation would be expected to provide a good approximation to exact GP regression.

PostScript [BibTex]

Williams, C., Rasmussen, C., Schwaighofer, A., Tresp, V. Observations on the Nyström Method for Gaussian Process Prediction Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2002 (techreport)

PostScript [BibTex]

2000

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Robust ensemble learning

Rätsch, G., Schölkopf, B., Smola, A., Mika, S., Onoda, T., Müller, K.

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)

[BibTex]

2000

Rätsch, G., Schölkopf, B., Smola, A., Mika, S., Onoda, T., Müller, K. 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)

[BibTex]

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Entropy numbers for convex combinations and MLPs

Smola, A., Elisseeff, A., Schölkopf, B., Williamson, R.

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)

[BibTex]

Smola, A., Elisseeff, A., Schölkopf, B., Williamson, R. 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)

[BibTex]

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Natural Regularization from Generative Models

Oliver, N., Schölkopf, B., Smola, A.

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)

[BibTex]

Oliver, N., Schölkopf, B., Smola, A. 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)

[BibTex]

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Solving Satisfiability Problems with Genetic Algorithms

Harmeling, S.

In Genetic Algorithms and Genetic Programming at Stanford 2000, pages: 206-213, (Editors: Koza, J. R.), Stanford Bookstore, Stanford, CA, USA, June 2000 (inbook)

Abstract
We show how to solve hard 3-SAT problems using genetic algorithms. Furthermore, we explore other genetic operators that may be useful to tackle 3-SAT problems, and discuss their pros and cons.

PDF [BibTex]

Harmeling, S. Solving Satisfiability Problems with Genetic Algorithms In Genetic Algorithms and Genetic Programming at Stanford 2000, pages: 206-213, (Editors: Koza, J. R.), Stanford Bookstore, Stanford, CA, USA, June 2000 (inbook)

PDF [BibTex]

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Statistical Learning and Kernel Methods

Schölkopf, B.

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)

[BibTex]

Schölkopf, B. 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)

[BibTex]

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An Introduction to Kernel-Based Learning Algorithms

Müller, K., Mika, S., Rätsch, G., Tsuda, K., Schölkopf, B.

In Handbook of Neural Network Signal Processing, 4, (Editors: Yu Hen Hu and Jang-Neng Hwang), CRC Press, 2000 (inbook)

[BibTex]

Müller, K., Mika, S., Rätsch, G., Tsuda, K., Schölkopf, B. 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)

[BibTex]

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The Kernel Trick for Distances

Schölkopf, B.

(MSR-TR-2000-51), Microsoft Research, Redmond, WA, USA, 2000 (techreport)

Abstract
A method is described which, like the kernel trick in support vector machines (SVMs), lets us generalize distance-based algorithms to operate in feature spaces, usually nonlinearly related to the input space. This is done by identifying a class of kernels which can be represented as normbased distances in Hilbert spaces. It turns out that common kernel algorithms, such as SVMs and kernel PCA, are actually really distance based algorithms and can be run with that class of kernels, too. As well as providing a useful new insight into how these algorithms work, the present work can form the basis for conceiving new algorithms.

PDF Web [BibTex]

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

PDF Web [BibTex]

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Kernel method for percentile feature extraction

Schölkopf, B., Platt, J., Smola, A.

(MSR-TR-2000-22), Microsoft Research, 2000 (techreport)

Abstract
A method is proposed which computes a direction in a dataset such that a speci􏰘ed fraction of a particular class of all examples is separated from the overall mean by a maximal margin􏰤 The pro jector onto that direction can be used for class􏰣speci􏰘c feature extraction􏰤 The algorithm is carried out in a feature space associated with a support vector kernel function􏰢 hence it can be used to construct a large class of nonlinear fea􏰣 ture extractors􏰤 In the particular case where there exists only one class􏰢 the method can be thought of as a robust form of principal component analysis􏰢 where instead of variance we maximize percentile thresholds􏰤 Fi􏰣 nally􏰢 we generalize it to also include the possibility of specifying negative examples􏰤

PDF [BibTex]

Schölkopf, B., Platt, J., Smola, A. Kernel method for percentile feature extraction (MSR-TR-2000-22), Microsoft Research, 2000 (techreport)

PDF [BibTex]