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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

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]

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]

Web [BibTex]


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Nonlinear Multivariate Analysis with Geodesic Kernels

Kuss, M.

Biologische Kybernetik, Technische Universität Berlin, February 2002 (diplomathesis)

GZIP [BibTex]

GZIP [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]

GZIP [BibTex]


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Concentration Inequalities and Empirical Processes Theory Applied to the Analysis of Learning Algorithms

Bousquet, O.

Biologische Kybernetik, Ecole Polytechnique, 2002 (phdthesis) Accepted

Abstract
New classification algorithms based on the notion of 'margin' (e.g. Support Vector Machines, Boosting) have recently been developed. The goal of this thesis is to better understand how they work, via a study of their theoretical performance. In order to do this, a general framework for real-valued classification is proposed. In this framework, it appears that the natural tools to use are Concentration Inequalities and Empirical Processes Theory. Thanks to an adaptation of these tools, a new measure of the size of a class of functions is introduced, which can be computed from the data. This allows, on the one hand, to better understand the role of eigenvalues of the kernel matrix in Support Vector Machines, and on the other hand, to obtain empirical model selection criteria.

PostScript [BibTex]


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Support Vector Machines: Induction Principle, Adaptive Tuning and Prior Knowledge

Chapelle, O.

Biologische Kybernetik, 2002 (phdthesis)

Abstract
This thesis presents a theoretical and practical study of Support Vector Machines (SVM) and related learning algorithms. In a first part, we introduce a new induction principle from which SVMs can be derived, but some new algorithms are also presented in this framework. In a second part, after studying how to estimate the generalization error of an SVM, we suggest to choose the kernel parameters of an SVM by minimizing this estimate. Several applications such as feature selection are presented. Finally the third part deals with the incoporation of prior knowledge in a learning algorithm and more specifically, we studied the case of known invariant transormations and the use of unlabeled data.

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]

[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]

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]

PostScript [BibTex]

1995


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A New Method for Constructing Artificial Neural Networks

Vapnik, V., Burges, C., Schölkopf, B.

AT & T Bell Laboratories, 1995 (techreport)

[BibTex]

1995

[BibTex]

1994


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View-based cognitive mapping and path planning

Schölkopf, B., Mallot, H.

(7), Max Planck Institute for Biological Cybernetics Tübingen, November 1994, This technical report has also been published elsewhere (techreport)

Abstract
We present a scheme for learning a cognitive map of a maze from a sequence of views and movement decisions. The scheme is based on an intermediate representation called the view graph. We show that this representation carries sufficient information to reconstruct the topological and directional structure of the maze. Moreover, we present a neural network that learns the view graph during a random exploration of the maze. We use a unsupervised competitive learning rule which translates temporal sequence (rather than similarity) of views into connectedness in the network. The network uses its knowledge of the topological and directional structure of the maze to generate expectations about which views are likely to be perceived next, improving the view recognition performance. We provide an additional mechanism which uses the map to find paths between arbitrary points of the previously explored environment. The results are compared to findings of behavioural neuroscience.

[BibTex]

1994

[BibTex]