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2002


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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]

2002

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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Application of Monte Carlo Methods to Psychometric Function Fitting

Wichmann, F.

Proceedings of the 33rd European Conference on Mathematical Psychology, pages: 44, 2002 (poster)

Abstract
The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. Here I describe methods to (1) fitting psychometric functions, (2) assessing goodness-of-fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them. First I describe a constrained maximum-likelihood method for parameter estimation. Using Monte-Carlo simulations I demonstrate that it is important to have a fitting method that takes stimulus-independent errors (or "lapses") into account. Second, a number of goodness-of-fit tests are introduced. Because psychophysical data sets are usually rather small I advocate the use of Monte Carlo resampling techniques that do not rely on asymptotic theory for goodness-of-fit assessment. Third, a parametric bootstrap is employed to estimate the variability of fitted parameters and derived quantities such as thresholds and slopes. I describe how the bootstrap bridging assumption, on which the validity of the procedure depends, can be tested without incurring too high a cost in computation time. Finally I describe how the methods can be extended to test hypotheses concerning the form and shape of several psychometric functions. Software describing the methods is available (http://www.bootstrap-software.com/psignifit/), as well as articles describing the methods in detail (Wichmann&Hill, Perception&Psychophysics, 2001a,b).

[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]


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Optimal linear estimation of self-motion - a real-world test of a model of fly tangential neurons

Franz, MO.

SAB 02 Workshop, Robotics as theoretical biology, 7th meeting of the International Society for Simulation of Adaptive Behaviour (SAB), (Editors: Prescott, T.; Webb, B.), 2002 (poster)

Abstract
The tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion (see example in Fig.1). We examine whether a simplified linear model of these neurons can be used to estimate self-motion from the optic flow. We present a theory for the construction of an optimal linear estimator incorporating prior knowledge both about the distance distribution of the environment, and about the noise and self-motion statistics of the sensor. The optimal estimator is tested on a gantry carrying an omnidirectional vision sensor that can be moved along three translational and one rotational degree of freedom. The experiments indicate that the proposed approach yields accurate results for rotation estimates, independently of the current translation and scene layout. Translation estimates, however, turned out to be sensitive to simultaneous rotation and to the particular distance distribution of the scene. The gantry experiments confirm that the receptive field organization of the tangential neurons allows them, as an ensemble, to extract self-motion from the optic flow.

PDF [BibTex]

PDF [BibTex]

1998


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Masking by plaid patterns: effects of presentation time and mask contrast

Wichmann, F., Henning, G.

pages: 115, 1. T{\"u}binger Wahrnehmungskonferenz (TWK 98), February 1998 (poster)

Abstract
Most current models of early spatial vision comprise of sets of orientation- and spatial-frequency selective filters with our without limited non-linear interactions amongst different subsets of the filters. The performance of human observers and of such models for human spatial vision were compared in experiments using maskers with two spatial frequencies (plaid masks). The detectability of horizontally orientated sinusoidal signals at 3.02 c/deg was measured in standard 2AFC-tasks in the presence of plaid patterns with two-components at the same spatial frequency as the signal but at different orientations (+/- 15, 30, 45, and 75 deg from the signal) and with varying contrasts (1.0, 6.25 and 25.0% contrast). In addition, the temporal envelope of the stimulus presentation was either a rectangular pulse of 19.7 msec duration, or a temporal Hanning window of 1497 msec.Threshold elevation varied with plaid component orientation, peaked +/- 30 deg from the signal where nearly a log unit threshold elevation for the 25.0% contrast plaid was observed. For plaids with 1.0% contrast we observed significant facilitation even with plaids whose components were 75 deg from that of the signal. Elevation factors were somewhat lower for the short stimulus presentation time but were still significant (up to a factor of 5 or 6). Despite of the simple nature of the stimuli employed in this study-sinusoidal signal and plaid masks comprised of only two sinusoids-none of the current models of early spatial vision can fully account for all the data gathered.

Web [BibTex]

1998

Web [BibTex]


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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]

[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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A bootstrap method for testing hypotheses concerning psychometric functions

Hill, N., Wichmann, F.

1998 (poster)

Abstract
Whenever psychometric functions are used to evaluate human performance on some task, it is valuable to examine not only the threshold and slope values estimated from the original data, but also the expected variability in those measures. This allows psychometric functions obtained in two experimental conditions to be compared statistically. We present a method for estimating the variability of thresholds and slopes of psychometric functions. This involves a maximum-likelihood fit to the data using a three-parameter mathematical function, followed by Monte Carlo simulation using the first fit as a generating function for the simulations. The variability of the function's parameters can then be estimated (as shown by Maloney, 1990), as can the variability of the threshold value (Foster & Bischof, 1997). We will show how a simple development of this procedure can be used to test the significance of differences between (a) the thresholds, and (b) the slopes of two psychometric functions. Further, our method can be used to assess the assumptions underlying the original fit, by examining how goodness-of-fit differs in simulation from its original value. In this way data sets can be identified as being either too noisy to be generated by a binomial observer, or significantly "too good to be true." All software is written in MATLAB and is therefore compatible across platforms, with the option of accelerating performance using MATLAB's plug-in binaries, or "MEX" files.

[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 methods in learning and feature extraction

Schölkopf, B., Smola, A., Müller, K., Burges, C., Vapnik, V.

Ninth Australian Conference on Neural Networks, pages: 72-78, (Editors: T. Downs, M. Frean and M. Gallagher), 1998 (talk)

[BibTex]

[BibTex]


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Support-Vektor-Lernen

Schölkopf, B.

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)

[BibTex]

[BibTex]


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Nonlinearities and the pedestal effect

Wichmann, F., Henning, G., Ploghaus, A.

Perception, 27, pages: S86, 1998 (poster)

Abstract
Psychophysical and physiological evidence suggests that luminance patterns are independently analysed in "channels" responding to different bands of spatial frequency. There are, however, interactions among stimuli falling well outside the usual estimates of channels' bandwidths (Henning, Hertz, and Broadbent, (1975). Vision Res., 15, 887-899). We examined whether the masking results of Henning et al. are consistent with independent channels. We postulated, before the channels, a point non-linearity which would introduce distortion products that might produce the observed interactions between stimuli two octaves apart in spatial frequency. Standard 2-AFC masking experiments determined whether possible distortion products of a 4.185 c/deg masking sinusoid revealed their presence through effects on the detection of a sinusoidal signal at the frequency of the second harmonic of the masker-8.37 c/deg. The signal and masker were horizontally orientated and the signal was in-phase, out-of-phase, or in quadrature with the putative second-order distortion product of the masker. Significant interactions between signal and masker were observed: for a wide range of masker contrasts, signal detection was facilitated by the masking stimulus. However, the shapes of the functions relating detection performance to masker contrast, as well as the effects of relative phase, were inconsistent with the notion that distortion products were responsible for the interactions observed.

[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]