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2012


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High Gamma-Power Predicts Performance in Brain-Computer Interfacing

Grosse-Wentrup, M., Schölkopf, B.

(3), Max-Planck-Institut für Intelligente Systeme, Tübingen, February 2012 (techreport)

Abstract
Subjects operating a brain-computer interface (BCI) based on sensorimotor rhythms exhibit large variations in performance over the course of an experimental session. Here, we show that high-frequency gamma-oscillations, originating in fronto-parietal networks, predict such variations on a trial-to-trial basis. We interpret this nding as empirical support for an in uence of attentional networks on BCI-performance via modulation of the sensorimotor rhythm.

PDF [BibTex]

2012

PDF [BibTex]


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Machine Learning and Interpretation in Neuroimaging - Revised Selected and Invited Contributions

Langs, G., Rish, I., Grosse-Wentrup, M., Murphy, B.

pages: 266, Springer, Heidelberg, Germany, International Workshop, MLINI, Held at NIPS, 2012, Lecture Notes in Computer Science, Vol. 7263 (proceedings)

DOI [BibTex]

DOI [BibTex]


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MICCAI, Workshop on Computational Diffusion MRI, 2012 (electronic publication)

Panagiotaki, E., O’Donnell, L., Schultz, T., Zhang, G.

15th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), Workshop on Computational Diffusion MRI , 2012 (proceedings)

PDF [BibTex]

PDF [BibTex]

2005


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Popper, Falsification and the VC-dimension

Corfield, D., Schölkopf, B., Vapnik, V.

(145), Max Planck Institute for Biological Cybernetics, November 2005 (techreport)

PDF [BibTex]

2005

PDF [BibTex]


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A Combinatorial View of Graph Laplacians

Huang, J.

(144), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2005 (techreport)

Abstract
Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties to Laplacian operators on continuous manifolds. There is still no strong proof on convergence for the normalized Laplacian. In this paper, we analyze different variants of graph Laplacians directly from the ways solving the original graph partitioning problem. The graph partitioning problem is a well-known combinatorial NP hard optimization problem. The spectral solutions provide evidence that normalized Laplacian encodes more reasonable considerations for graph partitioning. We also provide some examples to show their differences.

[BibTex]

[BibTex]


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Beyond Pairwise Classification and Clustering Using Hypergraphs

Zhou, D., Huang, J., Schölkopf, B.

(143), Max Planck Institute for Biological Cybernetics, August 2005 (techreport)

Abstract
In many applications, relationships among objects of interest are more complex than pairwise. Simply approximating complex relationships as pairwise ones can lead to loss of information. An alternative for these applications is to analyze complex relationships among data directly, without the need to first represent the complex relationships into pairwise ones. A natural way to describe complex relationships is to use hypergraphs. A hypergraph is a graph in which edges can connect more than two vertices. Thus we consider learning from a hypergraph, and develop a general framework which is applicable to classification and clustering for complex relational data. We have applied our framework to real-world web classification problems and obtained encouraging results.

PDF [BibTex]

PDF [BibTex]


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Generalized Nonnegative Matrix Approximations using Bregman Divergences

Sra, S., Dhillon, I.

Univ. of Texas at Austin, June 2005 (techreport)

[BibTex]

[BibTex]


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Measuring Statistical Dependence with Hilbert-Schmidt Norms

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

(140), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2005 (techreport)

Abstract
We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

PDF [BibTex]

PDF [BibTex]


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Consistency of Kernel Canonical Correlation Analysis

Fukumizu, K., Bach, F., Gretton, A.

(942), Institute of Statistical Mathematics, 4-6-7 Minami-azabu, Minato-ku, Tokyo 106-8569 Japan, June 2005 (techreport)

PDF [BibTex]

PDF [BibTex]


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Approximate Inference for Robust Gaussian Process Regression

Kuss, M., Pfingsten, T., Csato, L., Rasmussen, C.

(136), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract
Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectation-propagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectation-propagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling.

PDF [BibTex]

PDF [BibTex]


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Maximum-Margin Feature Combination for Detection and Categorization

BakIr, G., Wu, M., Eichhorn, J.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract
In this paper we are concerned with the optimal combination of features of possibly different types for detection and estimation tasks in machine vision. We propose to combine features such that the resulting classifier maximizes the margin between classes. In contrast to existing approaches which are non-convex and/or generative we propose to use a discriminative model leading to convex problem formulation and complexity control. Furthermore we assert that decision functions should not compare apples and oranges by comparing features of different types directly. Instead we propose to combine different similarity measures for each different feature type. Furthermore we argue that the question: ”Which feature type is more discriminative for task X?” is ill-posed and show empirically that the answer to this question might depend on the complexity of the decision function.

PDF [BibTex]

PDF [BibTex]


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Towards a Statistical Theory of Clustering. Presented at the PASCAL workshop on clustering, London

von Luxburg, U., Ben-David, S.

Presented at the PASCAL workshop on clustering, London, 2005 (techreport)

Abstract
The goal of this paper is to discuss statistical aspects of clustering in a framework where the data to be clustered has been sampled from some unknown probability distribution. Firstly, the clustering of the data set should reveal some structure of the underlying data rather than model artifacts due to the random sampling process. Secondly, the more sample points we have, the more reliable the clustering should be. We discuss which methods can and cannot be used to tackle those problems. In particular we argue that generalization bounds as they are used in statistical learning theory of classification are unsuitable in a general clustering framework. We suggest that the main replacements of generalization bounds should be convergence proofs and stability considerations. This paper should be considered as a road map paper which identifies important questions and potentially fruitful directions for future research about statistical clustering. We do not attempt to present a complete statistical theory of clustering.

PDF [BibTex]

PDF [BibTex]


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Approximate Bayesian Inference for Psychometric Functions using MCMC Sampling

Kuss, M., Jäkel, F., Wichmann, F.

(135), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract
In psychophysical studies the psychometric function is used to model the relation between the physical stimulus intensity and the observer's ability to detect or discriminate between stimuli of different intensities. In this report we propose the use of Bayesian inference to extract the information contained in experimental data estimate the parameters of psychometric functions. Since 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 parameterisation of psychometric functions and the role of prior distributions in the analysis. The proposed approach is exemplified using artificially generate d 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. The appendix provides a description of an implementation for the R environment for statistical computing and provides the code for reproducing the results discussed in the experiment section.

PDF [BibTex]

PDF [BibTex]

2001


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Kernel Methods for Extracting Local Image Semantics

Bradshaw, B., Schölkopf, B., Platt, J.

(MSR-TR-2001-99), Microsoft Research, October 2001 (techreport)

Web [BibTex]

2001

Web [BibTex]


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Calibration of Digital Amateur Cameras

Urbanek, M., Horaud, R., Sturm, P.

(RR-4214), INRIA Rhone Alpes, Montbonnot, France, July 2001 (techreport)

Web [BibTex]

Web [BibTex]


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Incorporating Invariances in Non-Linear Support Vector Machines

Chapelle, O., Schölkopf, B.

Max Planck Institute for Biological Cybernetics / Biowulf Technologies, 2001 (techreport)

Abstract
We consider the problem of how to incorporate in the Support Vector Machine (SVM) framework invariances given by some a priori known transformations under which the data should be invariant. It extends some previous work which was only applicable with linear SVMs and we show on a digit recognition task that the proposed approach is superior to the traditional Virtual Support Vector method.

PostScript [BibTex]

PostScript [BibTex]


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Bound on the Leave-One-Out Error for Density Support Estimation using nu-SVMs

Gretton, A., Herbrich, R., Schölkopf, B., Smola, A., Rayner, P.

University of Cambridge, 2001 (techreport)

[BibTex]

[BibTex]


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Bound on the Leave-One-Out Error for 2-Class Classification using nu-SVMs

Gretton, A., Herbrich, R., Schölkopf, B., Rayner, P.

University of Cambridge, 2001, Updated May 2003 (literature review expanded) (techreport)

Abstract
Three estimates of the leave-one-out error for $nu$-support vector (SV) machine binary classifiers are presented. Two of the estimates are based on the geometrical concept of the {em span}, which was introduced in the context of bounding the leave-one-out error for $C$-SV machine binary classifiers, while the third is based on optimisation over the criterion used to train the $nu$-support vector classifier. It is shown that the estimates presented herein provide informative and efficient approximations of the generalisation behaviour, in both a toy example and benchmark data sets. The proof strategies in the $nu$-SV context are also compared with those used to derive leave-one-out error estimates in the $C$-SV case.

PostScript [BibTex]

PostScript [BibTex]


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Inference Principles and Model Selection

Buhmann, J., Schölkopf, B.

(01301), Dagstuhl Seminar, 2001 (techreport)

Web [BibTex]

Web [BibTex]


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Some kernels for structured data

Bartlett, P., Schölkopf, B.

Biowulf Technologies, 2001 (techreport)

[BibTex]

[BibTex]

1998


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Generalization bounds and learning rates for Regularized principal manifolds

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

NeuroCOLT, 1998, NeuroColt2-TR 1998-027 (techreport)

[BibTex]

1998

[BibTex]


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Generalization Bounds for Convex Combinations of Kernel Functions

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

Royal Holloway College, 1998 (techreport)

[BibTex]

[BibTex]


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Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators

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

(19), NeuroCOLT, 1998, Accepted for publication in IEEE Transactions on Information Theory (techreport)

[BibTex]

[BibTex]


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Quantization Functionals and Regularized PrincipalManifolds

Smola, A., Mika, S., Schölkopf, B.

NeuroCOLT, 1998, NC2-TR-1998-028 (techreport)

[BibTex]

[BibTex]


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Support Vector Machine Reference Manual

Saunders, C., Stitson, M., Weston, J., Bottou, L., Schölkopf, B., Smola, A.

(CSD-TR-98-03), Department of Computer Science, Royal Holloway, University of London, 1998 (techreport)

PostScript [BibTex]

PostScript [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]