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2003


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Kernel Methods and Their Applications to Signal Processing

Bousquet, O., Perez-Cruz, F.

In Proceedings. (ICASSP ‘03), Special Session on Kernel Methods, pages: 860 , ICASSP, 2003 (inproceedings)

Abstract
Recently introduced in Machine Learning, the notion of kernels has drawn a lot of interest as it allows to obtain non-linear algorithms from linear ones in a simple and elegant manner. This, in conjunction with the introduction of new linear classification methods such as the Support Vector Machines has produced significant progress. The successes of such algorithms is now spreading as they are applied to more and more domains. Many Signal Processing problems, by their non-linear and high-dimensional nature may benefit from such techniques. We give an overview of kernel methods and their recent applications.

PDF PostScript [BibTex]

2003

PDF PostScript [BibTex]


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Predictive control with Gaussian process models

Kocijan, J., Murray-Smith, R., Rasmussen, CE., Likar, B.

In Proceedings of IEEE Region 8 Eurocon 2003: Computer as a Tool, pages: 352-356, (Editors: Zajc, B. and M. Tkal), Proceedings of IEEE Region 8 Eurocon: Computer as a Tool, 2003 (inproceedings)

Abstract
This paper describes model-based predictive control based on Gaussian processes.Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. It offers more insight in variance of obtained model response, as well as fewer parameters to determine than other models. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. This property is used in predictive control, where optimisation of control signal takes the variance information into account. The predictive control principle is demonstrated on a simulated example of nonlinear system.

PDF PostScript [BibTex]

PDF PostScript [BibTex]


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m-Alternative Forced Choice—Improving the Efficiency of the Method of Constant Stimuli

Jäkel, F.

Biologische Kybernetik, Graduate School for Neural and Behavioural Sciences, Tübingen, 2003 (diplomathesis)

[BibTex]

[BibTex]


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Distance-based classification with Lipschitz functions

von Luxburg, U., Bousquet, O.

In Learning Theory and Kernel Machines, Proceedings of the 16th Annual Conference on Computational Learning Theory, pages: 314-328, (Editors: Schölkopf, B. and M.K. Warmuth), Learning Theory and Kernel Machines, Proceedings of the 16th Annual Conference on Computational Learning Theory, 2003 (inproceedings)

Abstract
The goal of this article is to develop a framework for large margin classification in metric spaces. We want to find a generalization of linear decision functions for metric spaces and define a corresponding notion of margin such that the decision function separates the training points with a large margin. It will turn out that using Lipschitz functions as decision functions, the inverse of the Lipschitz constant can be interpreted as the size of a margin. In order to construct a clean mathematical setup we isometrically embed the given metric space into a Banach space and the space of Lipschitz functions into its dual space. Our approach leads to a general large margin algorithm for classification in metric spaces. To analyze this algorithm, we first prove a representer theorem. It states that there exists a solution which can be expressed as linear combination of distances to sets of training points. Then we analyze the Rademacher complexity of some Lipschitz function classes. The generality of the Lipschitz approach can be seen from the fact that several well-known algorithms are special cases of the Lipschitz algorithm, among them the support vector machine, the linear programming machine, and the 1-nearest neighbor classifier.

PDF PostScript [BibTex]

PDF PostScript [BibTex]


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Semi-Supervised Learning through Principal Directions Estimation

Chapelle, O., Schölkopf, B., Weston, J.

In ICML Workshop, The Continuum from Labeled to Unlabeled Data in Machine Learning & Data Mining, pages: 7, ICML Workshop: The Continuum from Labeled to Unlabeled Data in Machine Learning & Data Mining, 2003 (inproceedings)

Abstract
We describe methods for taking into account unlabeled data in the training of a kernel-based classifier, such as a Support Vector Machines (SVM). We propose two approaches utilizing unlabeled points in the vicinity of labeled ones. Both of the approaches effectively modify the metric of the pattern space, either by using non-spherical Gaussian density estimates which are determined using EM, or by modifying the kernel function using displacement vectors computed from pairs of unlabeled and labeled points. The latter is linked to techniques for training invariant SVMs. We present experimental results indicating that the proposed technique can lead to substantial improvements of classification accuracy.

PostScript [BibTex]

PostScript [BibTex]


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Machine Learning with Hyperkernels

Ong, CS., Smola, AJ.

In pages: 568-575, 2003 (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Gaussian Processes to Speed up Hybrid Monte Carlo for Expensive Bayesian Integrals

Rasmussen, CE.

In Bayesian Statistics 7, pages: 651-659, (Editors: J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West), Bayesian Statistics 7, 2003 (inproceedings)

Abstract
Hybrid Monte Carlo (HMC) is often the method of choice for computing Bayesian integrals that are not analytically tractable. However the success of this method may require a very large number of evaluations of the (un-normalized) posterior and its partial derivatives. In situations where the posterior is computationally costly to evaluate, this may lead to an unacceptable computational load for HMC. I propose to use a Gaussian Process model of the (log of the) posterior for most of the computations required by HMC. Within this scheme only occasional evaluation of the actual posterior is required to guarantee that the samples generated have exactly the desired distribution, even if the GP model is somewhat inaccurate. The method is demonstrated on a 10 dimensional problem, where 200 evaluations suffice for the generation of 100 roughly independent points from the posterior. Thus, the proposed scheme allows Bayesian treatment of models with posteriors that are computationally demanding, such as models involving computer simulation.

PDF PostScript Web [BibTex]

PDF PostScript Web [BibTex]


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Dimension Reduction Based on Orthogonality — a Decorrelation Method in ICA

Zhang, K., Chan, L.

In Artificial Neural Networks and Neural Information Processing - ICANN/ICONIP 2003, pages: 132-139, (Editors: O Kaynak and E Alpaydin and E Oja and L Xu), Springer, Berlin, Germany, International Conference on Artificial Neural Networks and International Conference on Neural Information Processing, ICANN/ICONIP, 2003, Lecture Notes in Computer Science, Volume 2714 (inproceedings)

Web DOI [BibTex]

Web DOI [BibTex]


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Models of contrast transfer as a function of presentation time and spatial frequency.

Wichmann, F.

2003 (poster)

Abstract
Understanding contrast transduction is essential for understanding spatial vision. Using standard 2AFC contrast discrimination experiments conducted using a carefully calibrated display we previously showed that the shape of the threshold versus (pedestal) contrast (TvC) curve changes with presentation time and the performance level defined as threshold (Wichmann, 1999; Wichmann & Henning, 1999). Additional experiments looked at the change of the TvC curve with spatial frequency (Bird, Henning & Wichmann, 2002), and at how to constrain the parameters of models of contrast processing (Wichmann, 2002). Here I report modelling results both across spatial frequency and presentation time. An extensive model-selection exploration was performed using Bayesian confidence regions for the fitted parameters as well as cross-validation methods. Bird, C.M., G.B. Henning and F.A. Wichmann (2002). Contrast discrimination with sinusoidal gratings of different spatial frequency. Journal of the Optical Society of America A, 19, 1267-1273. Wichmann, F.A. (1999). Some aspects of modelling human spatial vision: contrast discrimination. Unpublished doctoral dissertation, The University of Oxford. Wichmann, F.A. & Henning, G.B. (1999). Implications of the Pedestal Effect for Models of Contrast-Processing and Gain-Control. OSA Annual Meeting Program, 62. Wichmann, F.A. (2002). Modelling Contrast Transfer in Spatial Vision [Abstract]. Journal of Vision, 2, 7a.

[BibTex]