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2001


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An Introduction to Kernel-Based Learning Algorithms

Müller, K., Mika, S., Rätsch, G., Tsuda, K., Schölkopf, B.

IEEE Transactions on Neural Networks, 12(2):181-201, March 2001 (article)

Abstract
This paper provides an introduction to support vector machines, kernel Fisher discriminant analysis, and kernel principal component analysis, as examples for successful kernel-based learning methods. We first give a short background about Vapnik-Chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations. We illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and DNA analysis

DOI [BibTex]

2001

DOI [BibTex]


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Estimating the support of a high-dimensional distribution.

Schölkopf, B., Platt, J., Shawe-Taylor, J., Smola, A., Williamson, R.

Neural Computation, 13(7):1443-1471, March 2001 (article)

Abstract
Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a “simple” subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.

Web DOI [BibTex]

Web DOI [BibTex]


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The psychometric function: II. Bootstrap-based confidence intervals and sampling

Wichmann, F., Hill, N.

Perception and Psychophysics, 63 (8), pages: 1314-1329, 2001 (article)

PDF [BibTex]

PDF [BibTex]


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The psychometric function: I. Fitting, sampling and goodness-of-fit

Wichmann, F., Hill, N.

Perception and Psychophysics, 63 (8), pages: 1293-1313, 2001 (article)

Abstract
The psychometric function relates an observer'sperformance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function'sparameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (or lapses ). We show that failure to account for this can lead to serious biases in estimates of the psychometric function'sparameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditional X^2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods

PDF [BibTex]

PDF [BibTex]


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The control structure of artificial creatures

Zhou, D., Dai, R.

Artificial Life and Robotics, 5(3), 2001, invited article (article)

Web [BibTex]

Web [BibTex]


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Markovian domain fingerprinting: statistical segmentation of protein sequences

Bejerano, G., Seldin, Y., Margalit, H., Tishby, N.

Bioinformatics, 17(10):927-934, 2001 (article)

PDF Web [BibTex]

PDF Web [BibTex]

1999


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Lernen mit Kernen: Support-Vektor-Methoden zur Analyse hochdimensionaler Daten

Schölkopf, B., Müller, K., Smola, A.

Informatik - Forschung und Entwicklung, 14(3):154-163, September 1999 (article)

Abstract
We describe recent developments and results of statistical learning theory. In the framework of learning from examples, two factors control generalization ability: explaining the training data by a learning machine of a suitable complexity. We describe kernel algorithms in feature spaces as elegant and efficient methods of realizing such machines. Examples thereof are Support Vector Machines (SVM) and Kernel PCA (Principal Component Analysis). More important than any individual example of a kernel algorithm, however, is the insight that any algorithm that can be cast in terms of dot products can be generalized to a nonlinear setting using kernels. Finally, we illustrate the significance of kernel algorithms by briefly describing industrial and academic applications, including ones where we obtained benchmark record results.

PDF PDF DOI [BibTex]

1999

PDF PDF DOI [BibTex]


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Input space versus feature space in kernel-based methods

Schölkopf, B., Mika, S., Burges, C., Knirsch, P., Müller, K., Rätsch, G., Smola, A.

IEEE Transactions On Neural Networks, 10(5):1000-1017, September 1999 (article)

Abstract
This paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector (SV) kernel functions. We first discuss the geometry of feature space. In particular, we review what is known about the shape of the image of input space under the feature space map, and how this influences the capacity of SV methods. Following this, we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel, using the example of the class of inhomogeneous polynomial kernels, which are often used in SV pattern recognition. We then discuss the connection between feature space and input space by dealing with the question of how one can, given some vector in feature space, find a preimage (exact or approximate) in input space. We describe algorithms to tackle this issue, and show their utility in two applications of kernel methods. First, we use it to reduce the computational complexity of SV decision functions; second, we combine it with the kernel PCA algorithm, thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real-world data.

Web DOI [BibTex]

Web DOI [BibTex]


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p73 and p63 are homotetramers capable of weak heterotypic interactions with each other but not with p53.

Davison, T., Vagner, C., Kaghad, M., Ayed, A., Caput, D., CH, ..

Journal of Biological Chemistry, 274(26):18709-18714, June 1999 (article)

Abstract
Mutations in the p53 tumor suppressor gene are the most frequent genetic alterations found in human cancers. Recent identification of two human homologues of p53 has raised the prospect of functional interactions between family members via a conserved oligomerization domain. Here we report in vitro and in vivo analysis of homo- and hetero-oligomerization of p53 and its homologues, p63 and p73. The oligomerization domains of p63 and p73 can independently fold into stable homotetramers, as previously observed for p53. However, the oligomerization domain of p53 does not associate with that of either p73 or p63, even when p53 is in 15-fold excess. On the other hand, the oligomerization domains of p63 and p73 are able to weakly associate with one another in vitro. In vivo co-transfection assays of the ability of p53 and its homologues to activate reporter genes showed that a DNA-binding mutant of p53 was not able to act in a dominant negative manner over wild-type p73 or p63 but that a p73 mutant could inhibit the activity of wild-type p63. These data suggest that mutant p53 in cancer cells will not interact with endogenous or exogenous p63 or p73 via their respective oligomerization domains. It also establishes that the multiple isoforms of p63 as well as those of p73 are capable of interacting via their common oligomerization domain.

Web [BibTex]

Web [BibTex]


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Spatial Learning and Localization in Animals: A Computational Model and Its Implications for Mobile Robots

Balakrishnan, K., Bousquet, O., Honavar, V.

Adaptive Behavior, 7(2):173-216, 1999 (article)

[BibTex]


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SVMs for Histogram Based Image Classification

Chapelle, O., Haffner, P., Vapnik, V.

IEEE Transactions on Neural Networks, (9), 1999 (article)

Abstract
Traditional classification approaches generalize poorly on image classification tasks, because of the high dimensionality of the feature space. This paper shows that Support Vector Machines (SVM) can generalize well on difficult image classification problems where the only features are high dimensional histograms. Heavy-tailed RBF kernels of the form $K(mathbf{x},mathbf{y})=e^{-rhosum_i |x_i^a-y_i^a|^{b}}$ with $aleq 1$ and $b leq 2$ are evaluated on the classification of images extracted from the Corel Stock Photo Collection and shown to far outperform traditional polynomial or Gaussian RBF kernels. Moreover, we observed that a simple remapping of the input $x_i rightarrow x_i^a$ improves the performance of linear SVMs to such an extend that it makes them, for this problem, a valid alternative to RBF kernels.

GZIP [BibTex]

GZIP [BibTex]