Publications | Max Planck Institute for Intelligent Systems

42 results (View BibTeX file of all listed publications)

2005

Kernel Methods for Measuring Independence

Gretton, A., Herbrich, R., Smola, A., Bousquet, O., Schölkopf, B.

Journal of Machine Learning Research, 6, pages: 2075-2129, December 2005 (article)

Abstract

We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prove that when the RKHSs are universal, both functionals are zero if and only if the random variables are pairwise independent. We also show that the kernel mutual information is an upper bound near independence on the Parzen window estimate of the mutual information. Analogous results apply for two correlation-based dependence functionals introduced earlier: we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels, and prove the latter to be an upper bound on the mutual information near independence. The performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis.

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2005

ei Gretton, A., Herbrich, R., Smola, A., Bousquet, O., Schölkopf, B. Kernel Methods for Measuring Independence Journal of Machine Learning Research, 6, pages: 2075-2129, December 2005 (article)

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A Unifying View of Sparse Approximate Gaussian Process Regression

Quinonero Candela, J., Rasmussen, C.

Journal of Machine Learning Research, 6, pages: 1935-1959, December 2005 (article)

Abstract

We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the methods are using. This allows new insights to be gained, and highlights the relationship between existing methods. It also allows for a clear theoretically justified ranking of the closeness of the known approximations to the corresponding full GPs. Finally we point directly to designs of new better sparse approximations, combining the best of the existing strategies, within attractive computational constraints.

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ei Quinonero Candela, J., Rasmussen, C. A Unifying View of Sparse Approximate Gaussian Process Regression Journal of Machine Learning Research, 6, pages: 1935-1959, December 2005 (article)

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Maximal Margin Classification for Metric Spaces

Hein, M., Bousquet, O., Schölkopf, B.

Journal of Computer and System Sciences, 71(3):333-359, October 2005 (article)

Abstract

In order to apply the maximum margin method in arbitrary metric spaces, we suggest to embed the metric space into a Banach or Hilbert space and to perform linear classification in this space. We propose several embeddings and recall that an isometric embedding in a Banach space is always possible while an isometric embedding in a Hilbert space is only possible for certain metric spaces. As a result, we obtain a general maximum margin classification algorithm for arbitrary metric spaces (whose solution is approximated by an algorithm of Graepel. Interestingly enough, the embedding approach, when applied to a metric which can be embedded into a Hilbert space, yields the SVM algorithm, which emphasizes the fact that its solution depends on the metric and not on the kernel. Furthermore we give upper bounds of the capacity of the function classes corresponding to both embeddings in terms of Rademacher averages. Finally we compare the capacities of these function classes directly.

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ei Hein, M., Bousquet, O., Schölkopf, B. Maximal Margin Classification for Metric Spaces Journal of Computer and System Sciences, 71(3):333-359, October 2005 (article)

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Selective integration of multiple biological data for supervised network inference

Kato, T., Tsuda, K., Asai, K.

Bioinformatics, 21(10):2488 , October 2005 (article)

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ei Kato, T., Tsuda, K., Asai, K. Selective integration of multiple biological data for supervised network inference Bioinformatics, 21(10):2488 , October 2005 (article)

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Assessing Approximate Inference for Binary Gaussian Process Classification

Kuss, M., Rasmussen, C.

Journal of Machine Learning Research, 6, pages: 1679 , October 2005 (article)

Abstract

Gaussian process priors can be used to define flexible, probabilistic classification models. Unfortunately exact Bayesian inference is analytically intractable and various approximation techniques have been proposed. In this work we review and compare Laplace‘s method and Expectation Propagation for approximate Bayesian inference in the binary Gaussian process classification model. We present a comprehensive comparison of the approximations, their predictive performance and marginal likelihood estimates to results obtained by MCMC sampling. We explain theoretically and corroborate empirically the advantages of Expectation Propagation compared to Laplace‘s method.

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ei Kuss, M., Rasmussen, C. Assessing Approximate Inference for Binary Gaussian Process Classification Journal of Machine Learning Research, 6, pages: 1679 , October 2005 (article)

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Clustering on the Unit Hypersphere using von Mises-Fisher Distributions

Banerjee, A., Dhillon, I., Ghosh, J., Sra, S.

Journal of Machine Learning Research, 6, pages: 1345-1382, September 2005 (article)

Abstract

Several large scale data mining applications, such as text categorization and gene expression analysis, involve high-dimensional data that is also inherently directional in nature. Often such data is L2 normalized so that it lies on the surface of a unit hypersphere. Popular models such as (mixtures of) multi-variate Gaussians are inadequate for characterizing such data. This paper proposes a generative mixture-model approach to clustering directional data based on the von Mises-Fisher (vMF) distribution, which arises naturally for data distributed on the unit hypersphere. In particular, we derive and analyze two variants of the Expectation Maximization (EM) framework for estimating the mean and concentration parameters of this mixture. Numerical estimation of the concentration parameters is non-trivial in high dimensions since it involves functional inversion of ratios of Bessel functions. We also formulate two clustering algorithms corresponding to the variants of EM that we derive. Our approach provides a theoretical basis for the use of cosine similarity that has been widely employed by the information retrieval community, and obtains the spherical kmeans algorithm (kmeans with cosine similarity) as a special case of both variants. Empirical results on clustering of high-dimensional text and gene-expression data based on a mixture of vMF distributions show that the ability to estimate the concentration parameter for each vMF component, which is not present in existing approaches, yields superior results, especially for difficult clustering tasks in high-dimensional spaces.

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ei Banerjee, A., Dhillon, I., Ghosh, J., Sra, S. Clustering on the Unit Hypersphere using von Mises-Fisher Distributions Journal of Machine Learning Research, 6, pages: 1345-1382, September 2005 (article)

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Support Vector Machines for 3D Shape Processing

Steinke, F., Schölkopf, B., Blanz, V.

Computer Graphics Forum, 24(3, EUROGRAPHICS 2005):285-294, September 2005 (article)

Abstract

We propose statistical learning methods for approximating implicit surfaces and computing dense 3D deformation fields. Our approach is based on Support Vector (SV) Machines, which are state of the art in machine learning. It is straightforward to implement and computationally competitive; its parameters can be automatically set using standard machine learning methods. The surface approximation is based on a modified Support Vector regression. We present applications to 3D head reconstruction, including automatic removal of outliers and hole filling. In a second step, we build on our SV representation to compute dense 3D deformation fields between two objects. The fields are computed using a generalized SVMachine enforcing correspondence between the previously learned implicit SV object representations, as well as correspondences between feature points if such points are available. We apply the method to the morphing of 3D heads and other objects.

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ei Steinke, F., Schölkopf, B., Blanz, V. Support Vector Machines for 3D Shape Processing Computer Graphics Forum, 24(3, EUROGRAPHICS 2005):285-294, September 2005 (article)

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Fast Protein Classification with Multiple Networks

Tsuda, K., Shin, H., Schölkopf, B.

Bioinformatics, 21(Suppl. 2):59-65, September 2005 (article)

Abstract

Support vector machines (SVM) have been successfully used to classify proteins into functional categories. Recently, to integrate multiple data sources, a semidefinite programming (SDP) based SVM method was introduced Lanckriet et al (2004). In SDP/SVM, multiple kernel matrices corresponding to each of data sources are combined with weights obtained by solving an SDP. However, when trying to apply SDP/SVM to large problems, the computational cost can become prohibitive, since both converting the data to a kernel matrix for the SVM and solving the SDP are time and memory demanding. Another application-specific drawback arises when some of the data sources are protein networks. A common method of converting the network to a kernel matrix is the diffusion kernel method, which has time complexity of O(n^3), and produces a dense matrix of size n x n. We propose an efficient method of protein classification using multiple protein networks. Available protein networks, such as a physical interaction network or a metabolic network, can be directly incorporated. Vectorial data can also be incorporated after conversion into a network by means of neighbor point connection. Similarly to the SDP/SVM method, the combination weights are obtained by convex optimization. Due to the sparsity of network edges, the computation time is nearly linear in the number of edges of the combined network. Additionally, the combination weights provide information useful for discarding noisy or irrelevant networks. Experiments on function prediction of 3588 yeast proteins show promising results: the computation time is enormously reduced, while the accuracy is still comparable to the SDP/SVM method.

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ei Tsuda, K., Shin, H., Schölkopf, B. Fast Protein Classification with Multiple Networks Bioinformatics, 21(Suppl. 2):59-65, September 2005 (article)

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Iterative Kernel Principal Component Analysis for Image Modeling

Kim, K., Franz, M., Schölkopf, B.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(9):1351-1366, September 2005 (article)

Abstract

In recent years, Kernel Principal Component Analysis (KPCA) has been suggested for various image processing tasks requiring an image model such as, e.g., denoising or compression. The original form of KPCA, however, can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed. We therefore propose a new iterative method for performing KPCA, the Kernel Hebbian Algorithm which iteratively estimates the Kernel Principal Components with only linear order memory complexity. In our experiments, we compute models for complex image classes such as faces and natural images which require a large number of training examples. The resulting image models are tested in single-frame super-resolution and denoising applications. The KPCA model is not specifically tailored to these tasks; in fact, the same model can be used in super-resolution with variable input resolution, or denoising with unknown noise characteristics. In spite of this, both super-resolution a nd denoising performance are comparable to existing methods.

Web DOI [BibTex]

ei Kim, K., Franz, M., Schölkopf, B. Iterative Kernel Principal Component Analysis for Image Modeling IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(9):1351-1366, September 2005 (article)

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Phenotypic characterization of chondrosarcoma-derived cell lines

Schorle, C., Finger, F., Zien, A., Block, J., Gebhard, P., Aigner, T.

Cancer Letters, 226(2):143-154, August 2005 (article)

Abstract

Gene expression profiling of three chondrosarcoma derived cell lines (AD, SM, 105KC) showed an increased proliferative activity and a reduced expression of chondrocytic-typical matrix products compared to primary chondrocytes. The incapability to maintain an adequate matrix synthesis as well as a notable proliferative activity at the same time is comparable to neoplastic chondrosarcoma cells in vivo which cease largely cartilage matrix formation as soon as their proliferative activity increases. Thus, the investigated cell lines are of limited value as substitute of primary chondrocytes but might have a much higher potential to investigate the behavior of neoplastic chondrocytes, i.e. chondrosarcoma biology.

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ei Schorle, C., Finger, F., Zien, A., Block, J., Gebhard, P., Aigner, T. Phenotypic characterization of chondrosarcoma-derived cell lines Cancer Letters, 226(2):143-154, August 2005 (article)

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Local Rademacher Complexities

Bartlett, P., Bousquet, O., Mendelson, S.

The Annals of Statistics, 33(4):1497-1537, August 2005 (article)

Abstract

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present some applications to classification and prediction with convex function classes, and with kernel classes in particular.

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ei Bartlett, P., Bousquet, O., Mendelson, S. Local Rademacher Complexities The Annals of Statistics, 33(4):1497-1537, August 2005 (article)

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Learning the Kernel with Hyperkernels

Ong, CS., Smola, A., Williamson, R.

Journal of Machine Learning Research, 6, pages: 1043-1071, July 2005 (article)

Abstract

This paper addresses the problem of choosing a kernel suitable for estimation with a Support Vector Machine, hence further automating machine learning. This goal is achieved by defining a Reproducing Kernel Hilbert Space on the space of kernels itself. Such a formulation leads to a statistical estimation problem similar to the problem of minimizing a regularized risk functional. We state the equivalent representer theorem for the choice of kernels and present a semidefinite programming formulation of the resulting optimization problem. Several recipes for constructing hyperkernels are provided, as well as the details of common machine learning problems. Experimental results for classification, regression and novelty detection on UCI data show the feasibility of our approach.

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ei Ong, CS., Smola, A., Williamson, R. Learning the Kernel with Hyperkernels Journal of Machine Learning Research, 6, pages: 1043-1071, July 2005 (article)

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Image Reconstruction by Linear Programming

Tsuda, K., Rätsch, G.

IEEE Transactions on Image Processing, 14(6):737-744, June 2005 (article)

Abstract

One way of image denoising is to project a noisy image to the subspace of admissible images derived, for instance, by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion. We propose a new method to identify the noisy pixels by l1-norm penalization and to update the identified pixels only. The identification and updating of noisy pixels are formulated as one linear program which can be efficiently solved. In particular, one can apply the upsilon trick to directly specify the fraction of pixels to be reconstructed. Moreover, we extend the linear program to be able to exploit prior knowledge that occlusions often appear in contiguous blocks (e.g., sunglasses on faces). The basic idea is to penalize boundary points and interior points of the occluded area differently. We are also able to show the upsilon property for this extended LP leading to a method which is easy to use. Experimental results demonstrate the power of our approach.

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ei Tsuda, K., Rätsch, G. Image Reconstruction by Linear Programming IEEE Transactions on Image Processing, 14(6):737-744, June 2005 (article)

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RASE: recognition of alternatively spliced exons in C.elegans

Rätsch, G., Sonnenburg, S., Schölkopf, B.

Bioinformatics, 21(Suppl. 1):i369-i377, June 2005 (article)

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ei Rätsch, G., Sonnenburg, S., Schölkopf, B. RASE: recognition of alternatively spliced exons in C.elegans Bioinformatics, 21(Suppl. 1):i369-i377, June 2005 (article)

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Matrix Exponentiated Gradient Updates for On-line Learning and Bregman Projection

Tsuda, K., Rätsch, G., Warmuth, M.

Journal of Machine Learning Research, 6, pages: 995-1018, June 2005 (article)

Abstract

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: on-line learning with a simple square loss, and finding a symmetric positive definite matrix subject to linear constraints. The updates generalize the exponentiated gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponentials to preserve positive definiteness. Most importantly, we show how the derivation and the analyses of the original EG update and AdaBoost generalize to the non-diagonal case. We apply the resulting matrix exponentiated gradient (MEG) update and DefiniteBoost to the problem of learning a kernel matrix from distance measurements.

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ei Tsuda, K., Rätsch, G., Warmuth, M. Matrix Exponentiated Gradient Updates for On-line Learning and Bregman Projection Journal of Machine Learning Research, 6, pages: 995-1018, June 2005 (article)

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Texture and haptic cues in slant discrimination: Reliability-based cue weighting without statistically optimal cue combination

Rosas, P., Wagemans, J., Ernst, M., Wichmann, F.

Journal of the Optical Society of America A, 22(5):801-809, May 2005 (article)

Abstract

A number of models of depth cue combination suggest that the final depth percept results from a weighted average of independent depth estimates based on the different cues available. The weight of each cue in such an average is thought to depend on the reliability of each cue. In principle, such a depth estimation could be statistically optimal in the sense of producing the minimum variance unbiased estimator that can be constructed from the available information. Here we test such models using visual and haptic depth information. Different texture types produce differences in slant discrimination performance, providing a means for testing a reliability-sensitive cue combination model using texture as one of the cues to slant. Our results show that the weights for the cues were generally sensitive to their reliability, but fell short of statistically optimal combinationwe find reliability-based re-weighting, but not statistically optimal cue combination.

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ei Rosas, P., Wagemans, J., Ernst, M., Wichmann, F. Texture and haptic cues in slant discrimination: Reliability-based cue weighting without statistically optimal cue combination Journal of the Optical Society of America A, 22(5):801-809, May 2005 (article)

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Bayesian inference for psychometric functions

Kuss, M., Jäkel, F., Wichmann, F.

Journal of Vision, 5(5):478-492, May 2005 (article)

Abstract

In psychophysical studies, the psychometric function is used to model the relation between physical stimulus intensity and the observers ability to detect or discriminate between stimuli of different intensities. In this study, we propose the use of Bayesian inference to extract the information contained in experimental data to estimate the parameters of psychometric functions. Because Bayesian inference cannot be performed analytically, we describe how a Markov chain Monte Carlo method can be used to generate samples from the posterior distribution over parameters. These samples are used to estimate Bayesian confidence intervals and other characteristics of the posterior distribution. In addition, we discuss the parameterization of psychometric functions and the role of prior distributions in the analysis. The proposed approach is exemplified using artificially generated data and in a case study for real experimental data. Furthermore, we compare our approach with traditional methods based on maximum likelihood parameter estimation combined with bootstrap techniques for confidence interval estimation and find the Bayesian approach to be superior.

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ei Kuss, M., Jäkel, F., Wichmann, F. Bayesian inference for psychometric functions Journal of Vision, 5(5):478-492, May 2005 (article)

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A gene expression map of Arabidopsis thaliana development

Schmid, M., Davison, T., Henz, S., Pape, U., Demar, M., Vingron, M., Schölkopf, B., Weigel, D., Lohmann, J.

Nature Genetics, 37(5):501-506, April 2005 (article)

Abstract

Regulatory regions of plant genes tend to be more compact than those of animal genes, but the complement of transcription factors encoded in plant genomes is as large or larger than that found in those of animals. Plants therefore provide an opportunity to study how transcriptional programs control multicellular development. We analyzed global gene expression during development of the reference plant Arabidopsis thaliana in samples covering many stages, from embryogenesis to senescence, and diverse organs. Here, we provide a first analysis of this data set, which is part of the AtGenExpress expression atlas. We observed that the expression levels of transcription factor genes and signal transduction components are similar to those of metabolic genes. Examining the expression patterns of large gene families, we found that they are often more similar than would be expected by chance, indicating that many gene families have been co-opted for specific developmental processes.

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ei Schmid, M., Davison, T., Henz, S., Pape, U., Demar, M., Vingron, M., Schölkopf, B., Weigel, D., Lohmann, J. A gene expression map of Arabidopsis thaliana development Nature Genetics, 37(5):501-506, April 2005 (article)

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Experimentally optimal v in support vector regression for different noise models and parameter settings

Chalimourda, A., Schölkopf, B., Smola, A.

Neural Networks, 18(2):205-205, March 2005 (article)

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ei Chalimourda, A., Schölkopf, B., Smola, A. Experimentally optimal v in support vector regression for different noise models and parameter settings Neural Networks, 18(2):205-205, March 2005 (article)

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Invariance of Neighborhood Relation under Input Space to Feature Space Mapping

Shin, H., Cho, S.

Pattern Recognition Letters, 26(6):707-718, 2005 (article)

Abstract

If the training pattern set is large, it takes a large memory and a long time to train support vector machine (SVM). Recently, we proposed neighborhood property based pattern selection algorithm (NPPS) which selects only the patterns that are likely to be near the decision boundary ahead of SVM training [Proc. of the 7th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), Lecture Notes in Artificial Intelligence (LNAI 2637), Seoul, Korea, pp. 376387]. NPPS tries to identify those patterns that are likely to become support vectors in feature space. Preliminary reports show its effectiveness: SVM training time was reduced by two orders of magnitude with almost no loss in accuracy for various datasets. It has to be noted, however, that decision boundary of SVM and support vectors are all defined in feature space while NPPS described above operates in input space. If neighborhood relation in input space is not preserved in feature space, NPPS may not always be effective. In this paper, we sh ow that the neighborhood relation is invariant under input to feature space mapping. The result assures that the patterns selected by NPPS in input space are likely to be located near decision boundary in feature space.

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ei Shin, H., Cho, S. Invariance of Neighborhood Relation under Input Space to Feature Space Mapping Pattern Recognition Letters, 26(6):707-718, 2005 (article)

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Theory of Classification: A Survey of Some Recent Advances

Boucheron, S., Bousquet, O., Lugosi, G.

ESAIM: Probability and Statistics, 9, pages: 323 , 2005 (article)

Abstract

The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have lead to these important recent developments.

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ei Boucheron, S., Bousquet, O., Lugosi, G. Theory of Classification: A Survey of Some Recent Advances ESAIM: Probability and Statistics, 9, pages: 323 , 2005 (article)

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Support Vector Machines and Kernel Algorithms

Schölkopf, B., Smola, A.

In Encyclopedia of Biostatistics (2nd edition), Vol. 8, 8, pages: 5328-5335, (Editors: P Armitage and T Colton), John Wiley & Sons, NY USA, 2005 (inbook)

[BibTex]

ei Schölkopf, B., Smola, A. Support Vector Machines and Kernel Algorithms In Encyclopedia of Biostatistics (2nd edition), Vol. 8, 8, pages: 5328-5335, (Editors: P Armitage and T Colton), John Wiley & Sons, NY USA, 2005 (inbook)

[BibTex]

Moment Inequalities for Functions of Independent Random Variables

Boucheron, S., Bousquet, O., Lugosi, G., Massart, P.

To appear in Annals of Probability, 33, pages: 514-560, 2005 (article)

Abstract

A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions cite{BoLuMa01}, and is based on a generalized tensorization inequality due to Lata{l}a and Oleszkiewicz cite{LaOl00}. The new inequalities prove to be a versatile tool in a wide range of applications. We illustrate the power of the method by showing how it can be used to effortlessly re-derive classical inequalities including Rosenthal and Kahane-Khinchine-type inequalities for sums of independent random variables, moment inequalities for suprema of empirical processes, and moment inequalities for Rademacher chaos and $U$-statistics. Some of these corollaries are apparently new. In particular, we generalize Talagrands exponential inequality for Rademacher chaos of order two to any order. We also discuss applications for other complex functions of independent random variables, such as suprema of boolean polynomials which include, as special cases, subgraph counting problems in random graphs.

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ei Boucheron, S., Bousquet, O., Lugosi, G., Massart, P. Moment Inequalities for Functions of Independent Random Variables To appear in Annals of Probability, 33, pages: 514-560, 2005 (article)

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Visual perception I: Basic principles

Wagemans, J., Wichmann, F., de Beeck, H.

In Handbook of Cognition, pages: 3-47, (Editors: Lamberts, K. , R. Goldstone), Sage, London, 2005 (inbook)

[BibTex]

ei Wagemans, J., Wichmann, F., de Beeck, H. Visual perception I: Basic principles In Handbook of Cognition, pages: 3-47, (Editors: Lamberts, K. , R. Goldstone), Sage, London, 2005 (inbook)

[BibTex]

A tutorial on v-support vector machines

Chen, P., Lin, C., Schölkopf, B.

Applied Stochastic Models in Business and Industry, 21(2):111-136, 2005 (article)

Abstract

We briefly describe the main ideas of statistical learning theory, support vector machines (SVMs), and kernel feature spaces. We place particular emphasis on a description of the so-called -SVM, including details of the algorithm and its implementation, theoretical results, and practical applications. Copyright © 2005 John Wiley & Sons, Ltd.

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ei Chen, P., Lin, C., Schölkopf, B. A tutorial on v-support vector machines Applied Stochastic Models in Business and Industry, 21(2):111-136, 2005 (article)

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Robust EEG Channel Selection Across Subjects for Brain Computer Interfaces

Schröder, M., Lal, T., Hinterberger, T., Bogdan, M., Hill, J., Birbaumer, N., Rosenstiel, W., Schölkopf, B.

EURASIP Journal on Applied Signal Processing, 2005(19, Special Issue: Trends in Brain Computer Interfaces):3103-3112, (Editors: Vesin, J. M., T. Ebrahimi), 2005 (article)

Abstract

Most EEG-based Brain Computer Interface (BCI) paradigms come along with specific electrode positions, e.g.~for a visual based BCI electrode positions close to the primary visual cortex are used. For new BCI paradigms it is usually not known where task relevant activity can be measured from the scalp. For individual subjects Lal et.~al showed that recording positions can be found without the use of prior knowledge about the paradigm used. However it remains unclear to what extend their method of Recursive Channel Elimination (RCE) can be generalized across subjects. In this paper we transfer channel rankings from a group of subjects to a new subject. For motor imagery tasks the results are promising, although cross-subject channel selection does not quite achieve the performance of channel selection on data of single subjects. Although the RCE method was not provided with prior knowledge about the mental task, channels that are well known to be important (from a physiological point of view) were consistently selected whereas task-irrelevant channels were reliably disregarded.

Web DOI [BibTex]

ei Schröder, M., Lal, T., Hinterberger, T., Bogdan, M., Hill, J., Birbaumer, N., Rosenstiel, W., Schölkopf, B. Robust EEG Channel Selection Across Subjects for Brain Computer Interfaces EURASIP Journal on Applied Signal Processing, 2005(19, Special Issue: Trends in Brain Computer Interfaces):3103-3112, (Editors: Vesin, J. M., T. Ebrahimi), 2005 (article)

Web DOI [BibTex]

2003

Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

Bousquet, O.

Stochastic Inequalities and Applications, 56, pages: 213-247, Progress in Probability, (Editors: Giné, E., C. Houdré and D. Nualart), November 2003 (article)

Abstract

We obtain exponential concentration inequalities for sub-additive functions of independent random variables under weak conditions on the increments of those functions, like the existence of exponential moments for these increments. As a consequence of these general inequalities, we obtain refinements of Talagrand's inequality for empirical processes and new bounds for randomized empirical processes. These results are obtained by further developing the entropy method introduced by Ledoux.

PostScript [BibTex]

2003

ei Bousquet, O. Concentration Inequalities for Sub-Additive Functions Using the Entropy Method Stochastic Inequalities and Applications, 56, pages: 213-247, Progress in Probability, (Editors: Giné, E., C. Houdré and D. Nualart), November 2003 (article)

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Statistical Learning Theory, Capacity and Complexity

Schölkopf, B.

Complexity, 8(4):87-94, July 2003 (article)

Abstract

We give an exposition of the ideas of statistical learning theory, followed by a discussion of how a reinterpretation of the insights of learning theory could potentially also benefit our understanding of a certain notion of complexity.

Web DOI [BibTex]

ei Schölkopf, B. Statistical Learning Theory, Capacity and Complexity Complexity, 8(4):87-94, July 2003 (article)

Web DOI [BibTex]

Dealing with large Diagonals in Kernel Matrices

Weston, J., Schölkopf, B., Eskin, E., Leslie, C., Noble, W.

Annals of the Institute of Statistical Mathematics, 55(2):391-408, June 2003 (article)

Abstract

In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well: We propose and test several methods for dealing with this problem by reducing the dynamic range of the matrix while preserving the positive definiteness of the Hessian of the quadratic programming problem that one has to solve when training a Support Vector Machine, which is a common kernel approach for pattern recognition.

PDF DOI [BibTex]

ei Weston, J., Schölkopf, B., Eskin, E., Leslie, C., Noble, W. Dealing with large Diagonals in Kernel Matrices Annals of the Institute of Statistical Mathematics, 55(2):391-408, June 2003 (article)

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The em Algorithm for Kernel Matrix Completion with Auxiliary Data

Tsuda, K., Akaho, S., Asai, K.

Journal of Machine Learning Research, 4, pages: 67-81, May 2003 (article)

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ei Tsuda, K., Akaho, S., Asai, K. The em Algorithm for Kernel Matrix Completion with Auxiliary Data Journal of Machine Learning Research, 4, pages: 67-81, May 2003 (article)

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Constructing Descriptive and Discriminative Non-linear Features: Rayleigh Coefficients in Kernel Feature Spaces

Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Smola, A., Müller, K.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(5):623-628, May 2003 (article)

Abstract

We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher‘s discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.

DOI [BibTex]

ei Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Smola, A., Müller, K. Constructing Descriptive and Discriminative Non-linear Features: Rayleigh Coefficients in Kernel Feature Spaces IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(5):623-628, May 2003 (article)

DOI [BibTex]

Tractable Inference for Probabilistic Data Models

Csato, L., Opper, M., Winther, O.

Complexity, 8(4):64-68, April 2003 (article)

Abstract

We present an approximation technique for probabilistic data models with a large number of hidden variables, based on ideas from statistical physics. We give examples for two nontrivial applications. © 2003 Wiley Periodicals, Inc.

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ei Csato, L., Opper, M., Winther, O. Tractable Inference for Probabilistic Data Models Complexity, 8(4):64-68, April 2003 (article)

PDF GZIP Web [BibTex]

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.

Bioinformatics, 19(6):764-771, April 2003 (article)

Abstract

Motivation: In drug discovery a key task is to identify characteristics that separate active (binding) compounds from inactive (non-binding) ones. An automated prediction system can help reduce resources necessary to carry out this task. Results: Two methods for prediction of molecular bioactivity for drug design are introduced and shown to perform well in a data set previously studied as part of the KDD (Knowledge Discovery and Data Mining) Cup 2001. The data is characterized by very few positive examples, a very large number of features (describing three-dimensional properties of the molecules) and rather different distributions between training and test data. Two techniques are introduced specifically to tackle these problems: a feature selection method for unbalanced data and a classifier which adapts to the distribution of the the unlabeled test data (a so-called transductive method). We show both techniques improve identification performance and in conjunction provide an improvement over using only one of the techniques. Our results suggest the importance of taking into account the characteristics in this data which may also be relevant in other problems of a similar type.

Web [BibTex]

ei 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 Bioinformatics, 19(6):764-771, April 2003 (article)

Web [BibTex]

Use of the Zero-Norm with Linear Models and Kernel Methods

Weston, J., Elisseeff, A., Schölkopf, B., Tipping, M.

Journal of Machine Learning Research, 3, pages: 1439-1461, March 2003 (article)

Abstract

We explore the use of the so-called zero-norm of the parameters of linear models in learning. Minimization of such a quantity has many uses in a machine learning context: for variable or feature selection, minimizing training error and ensuring sparsity in solutions. We derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero-norm. The method boils down to implementing a simple modification of vanilla SVM, namely via an iterative multiplicative rescaling of the training data. Applications we investigate which aid our discussion include variable and feature selection on biological microarray data, and multicategory classification.

PDF PostScript PDF [BibTex]

ei Weston, J., Elisseeff, A., Schölkopf, B., Tipping, M. Use of the Zero-Norm with Linear Models and Kernel Methods Journal of Machine Learning Research, 3, pages: 1439-1461, March 2003 (article)

PDF PostScript PDF [BibTex]

An Introduction to Variable and Feature Selection.

Guyon, I., Elisseeff, A.

Journal of Machine Learning, 3, pages: 1157-1182, 2003 (article)

[BibTex]

ei Guyon, I., Elisseeff, A. An Introduction to Variable and Feature Selection. Journal of Machine Learning, 3, pages: 1157-1182, 2003 (article)

[BibTex]

Extension of the nu-SVM range for classification

Perez-Cruz, F., Weston, J., Herrmann, D., Schölkopf, B.

In Advances in Learning Theory: Methods, Models and Applications, NATO Science Series III: Computer and Systems Sciences, Vol. 190, 190, pages: 179-196, NATO Science Series III: Computer and Systems Sciences, (Editors: J Suykens and G Horvath and S Basu and C Micchelli and J Vandewalle), IOS Press, Amsterdam, 2003 (inbook)

[BibTex]

ei Perez-Cruz, F., Weston, J., Herrmann, D., Schölkopf, B. Extension of the nu-SVM range for classification In Advances in Learning Theory: Methods, Models and Applications, NATO Science Series III: Computer and Systems Sciences, Vol. 190, 190, pages: 179-196, NATO Science Series III: Computer and Systems Sciences, (Editors: J Suykens and G Horvath and S Basu and C Micchelli and J Vandewalle), IOS Press, Amsterdam, 2003 (inbook)

[BibTex]

New Approaches to Statistical Learning Theory

Bousquet, O.

Annals of the Institute of Statistical Mathematics, 55(2):371-389, 2003 (article)

Abstract

We present new tools from probability theory that can be applied to the analysis of learning algorithms. These tools allow to derive new bounds on the generalization performance of learning algorithms and to propose alternative measures of the complexity of the learning task, which in turn can be used to derive new learning algorithms.

PostScript [BibTex]

ei Bousquet, O. New Approaches to Statistical Learning Theory Annals of the Institute of Statistical Mathematics, 55(2):371-389, 2003 (article)

PostScript [BibTex]

An Introduction to Support Vector Machines

Schölkopf, B.

In Recent Advances and Trends in Nonparametric Statistics , pages: 3-17, (Editors: MG Akritas and DN Politis), Elsevier, Amsterdam, The Netherlands, 2003 (inbook)

Web DOI [BibTex]

ei Schölkopf, B. An Introduction to Support Vector Machines In Recent Advances and Trends in Nonparametric Statistics , pages: 3-17, (Editors: MG Akritas and DN Politis), Elsevier, Amsterdam, The Netherlands, 2003 (inbook)

Web DOI [BibTex]

Statistical Learning and Kernel Methods in Bioinformatics

Schölkopf, B., Guyon, I., Weston, J.

In Artificial Intelligence and Heuristic Methods in Bioinformatics, 183, pages: 1-21, 3, (Editors: P Frasconi und R Shamir), IOS Press, Amsterdam, The Netherlands, 2003 (inbook)

[BibTex]

ei Schölkopf, B., Guyon, I., Weston, J. Statistical Learning and Kernel Methods in Bioinformatics In Artificial Intelligence and Heuristic Methods in Bioinformatics, 183, pages: 1-21, 3, (Editors: P Frasconi und R Shamir), IOS Press, Amsterdam, The Netherlands, 2003 (inbook)

[BibTex]

A Short Introduction to Learning with Kernels

Schölkopf, B., Smola, A.

In Proceedings of the Machine Learning Summer School, Lecture Notes in Artificial Intelligence, Vol. 2600, pages: 41-64, LNAI 2600, (Editors: S Mendelson and AJ Smola), Springer, Berlin, Heidelberg, Germany, 2003 (inbook)

[BibTex]

ei Schölkopf, B., Smola, A. A Short Introduction to Learning with Kernels In Proceedings of the Machine Learning Summer School, Lecture Notes in Artificial Intelligence, Vol. 2600, pages: 41-64, LNAI 2600, (Editors: S Mendelson and AJ Smola), Springer, Berlin, Heidelberg, Germany, 2003 (inbook)

[BibTex]

Bayesian Kernel Methods

Smola, A., Schölkopf, B.

In Advanced Lectures on Machine Learning, Machine Learning Summer School 2002, Lecture Notes in Computer Science, Vol. 2600, LNAI 2600, pages: 65-117, 0, (Editors: S Mendelson and AJ Smola), Springer, Berlin, Germany, 2003 (inbook)

DOI [BibTex]

ei Smola, A., Schölkopf, B. Bayesian Kernel Methods In Advanced Lectures on Machine Learning, Machine Learning Summer School 2002, Lecture Notes in Computer Science, Vol. 2600, LNAI 2600, pages: 65-117, 0, (Editors: S Mendelson and AJ Smola), Springer, Berlin, Germany, 2003 (inbook)

DOI [BibTex]

Stability of ensembles of kernel machines

Elisseeff, A., Pontil, M.

In 190, pages: 111-124, NATO Science Series III: Computer and Systems Science, (Editors: Suykens, J., G. Horvath, S. Basu, C. Micchelli and J. Vandewalle), IOS press, Netherlands, 2003 (inbook)

[BibTex]

ei Elisseeff, A., Pontil, M. Stability of ensembles of kernel machines In 190, pages: 111-124, NATO Science Series III: Computer and Systems Science, (Editors: Suykens, J., G. Horvath, S. Basu, C. Micchelli and J. Vandewalle), IOS press, Netherlands, 2003 (inbook)

[BibTex]

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