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2009


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Learning an Interactive Segmentation System

Nickisch, H., Kohli, P., Rother, C.

Max Planck Institute for Biological Cybernetics, December 2009 (techreport)

Abstract
Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluated by computing the accuracy of their solutions under some fixed set of user interactions. This paper proposes a new evaluation and learning method which brings the user in the loop. It is based on the use of an active robot user - a simulated model of a human user. We show how this approach can be used to evaluate and learn parameters of state-of-the-art interactive segmentation systems. We also show how simulated user models can be integrated into the popular max-margin method for parameter learning and propose an algorithm to solve the resulting optimisation problem.

Web [BibTex]

2009

Web [BibTex]


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Machine Learning for Brain-Computer Interfaces

Hill, NJ.

Mini-Symposia on Assistive Machine Learning for People with Disabilities at NIPS (AMD), December 2009 (talk)

Abstract
Brain-computer interfaces (BCI) aim to be the ultimate in assistive technology: decoding a user‘s intentions directly from brain signals without involving any muscles or peripheral nerves. Thus, some classes of BCI potentially offer hope for users with even the most extreme cases of paralysis, such as in late-stage Amyotrophic Lateral Sclerosis, where nothing else currently allows communication of any kind. Other lines in BCI research aim to restore lost motor function in as natural a way as possible, reconnecting and in some cases re-training motor-cortical areas to control prosthetic, or previously paretic, limbs. Research and development are progressing on both invasive and non-invasive fronts, although BCI has yet to make a breakthrough to widespread clinical application. The high-noise high-dimensional nature of brain-signals, particularly in non-invasive approaches and in patient populations, make robust decoding techniques a necessity. Generally, the approach has been to use relatively simple feature extraction techniques, such as template matching and band-power estimation, coupled to simple linear classifiers. This has led to a prevailing view among applied BCI researchers that (sophisticated) machine-learning is irrelevant since "it doesn‘t matter what classifier you use once you‘ve done your preprocessing right and extracted the right features." I shall show a few examples of how this runs counter to both the empirical reality and the spirit of what needs to be done to bring BCI into clinical application. Along the way I‘ll highlight some of the interesting problems that remain open for machine-learners.

PDF Web Web [BibTex]

PDF Web Web [BibTex]


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PAC-Bayesian Approach to Formulation of Clustering Objectives

Seldin, Y.

NIPS Workshop on "Clustering: Science or Art? Towards Principled Approaches", December 2009 (talk)

Abstract
Clustering is a widely used tool for exploratory data analysis. However, the theoretical understanding of clustering is very limited. We still do not have a well-founded answer to the seemingly simple question of "how many clusters are present in the data?", and furthermore a formal comparison of clusterings based on different optimization objectives is far beyond our abilities. The lack of good theoretical support gives rise to multiple heuristics that confuse the practitioners and stall development of the field. We suggest that the ill-posed nature of clustering problems is caused by the fact that clustering is often taken out of its subsequent application context. We argue that one does not cluster the data just for the sake of clustering it, but rather to facilitate the solution of some higher level task. By evaluation of the clustering‘s contribution to the solution of the higher level task it is possible to compare different clusterings, even those obtained by different optimization objectives. In the preceding work it was shown that such an approach can be applied to evaluation and design of co-clustering solutions. Here we suggest that this approach can be extended to other settings, where clustering is applied.

PDF Web Web [BibTex]

PDF Web Web [BibTex]


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Semi-supervised Kernel Canonical Correlation Analysis of Human Functional Magnetic Resonance Imaging Data

Shelton, JA.

Women in Machine Learning Workshop (WiML), December 2009 (talk)

Abstract
Kernel Canonical Correlation Analysis (KCCA) is a general technique for subspace learning that incorporates principal components analysis (PCA) and Fisher linear discriminant analysis (LDA) as special cases. By finding directions that maximize correlation, KCCA learns representations tied more closely to underlying process generating the the data and can ignore high-variance noise directions. However, for data where acquisition in a given modality is expensive or otherwise limited, KCCA may suffer from small sample effects. We propose to use semi-supervised Laplacian regularization to utilize data that are present in only one modality. This manifold learning approach is able to find highly correlated directions that also lie along the data manifold, resulting in a more robust estimate of correlated subspaces. Functional magnetic resonance imaging (fMRI) acquired data are naturally amenable to subspace techniques as data are well aligned and such data of the human brain are a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single and multivariate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, Laplacian regularization improved performance whereas the semi-supervised variants of KCCA yielded the best performance. We additionally analyze the weights learned by the regression in order to infer brain regions that are important during different types of visual processing.

PDF Web [BibTex]


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Detection of objects in noisy images and site percolation on square lattices

Langovoy, M., Wittich, O.

(2009-035), EURANDOM, Technische Universiteit Eindhoven, November 2009 (techreport)

Abstract
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. Our procedure substantially differs from wavelets-based algorithms. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.

PDF [BibTex]

PDF [BibTex]


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An Incremental GEM Framework for Multiframe Blind Deconvolution, Super-Resolution, and Saturation Correction

Harmeling, S., Sra, S., Hirsch, M., Schölkopf, B.

(187), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

Abstract
We develop an incremental generalized expectation maximization (GEM) framework to model the multiframe blind deconvolution problem. A simplistic version of this problem was recently studied by Harmeling etal~cite{harmeling09}. We solve a more realistic version of this problem which includes the following major features: (i) super-resolution ability emph{despite} noise and unknown blurring; (ii) saturation-correction, i.e., handling of overexposed pixels that can otherwise confound the image processing; and (iii) simultaneous handling of color channels. These features are seamlessly integrated into our incremental GEM framework to yield simple but efficient multiframe blind deconvolution algorithms. We present technical details concerning critical steps of our algorithms, especially to highlight how all operations can be written using matrix-vector multiplications. We apply our algorithm to real-world images from astronomy and super resolution tasks. Our experimental results show that our methods yield improve d resolution and deconvolution at the same time.

PDF [BibTex]

PDF [BibTex]


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Efficient Filter Flow for Space-Variant Multiframe Blind Deconvolution

Hirsch, M., Sra, S., Schölkopf, B., Harmeling, S.

(188), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

Abstract
Ultimately being motivated by facilitating space-variant blind deconvolution, we present a class of linear transformations, that are expressive enough for space-variant filters, but at the same time especially designed for efficient matrix-vector-multiplications. Successful results on astronomical imaging through atmospheric turbulences and on noisy magnetic resonance images of constantly moving objects demonstrate the practical significance of our approach.

PDF [BibTex]

PDF [BibTex]


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Event-Related Potentials in Brain-Computer Interfacing

Hill, NJ.

Invited lecture on the bachelor & masters course "Introduction to Brain-Computer Interfacing", October 2009 (talk)

Abstract
An introduction to event-related potentials with specific reference to their use in brain-computer interfacing applications and research.

PDF [BibTex]

PDF [BibTex]


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BCI2000 and Python

Hill, NJ.

Invited lecture at the 5th International BCI2000 Workshop, October 2009 (talk)

Abstract
A tutorial, with exercises, on how to integrate your own Python code with the BCI2000 software package.

PDF [BibTex]

PDF [BibTex]


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Implementing a Signal Processing Filter in BCI2000 Using C++

Hill, NJ., Mellinger, J.

Invited lecture at the 5th International BCI2000 Workshop, October 2009 (talk)

Abstract
This tutorial shows how the functionality of the BCI2000 software package can be extended with one‘s own code, using BCI2000‘s C++ API.

PDF [BibTex]

PDF [BibTex]


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Algebraic polynomials and moments of stochastic integrals

Langovoy, M.

(2009-031), EURANDOM, Technische Universiteit Eindhoven, October 2009 (techreport)

PDF [BibTex]

PDF [BibTex]


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Kernel Learning Approaches for Image Classification

Gehler, PV.

Biologische Kybernetik, Universität des Saarlandes, Saarbrücken, Germany, October 2009 (phdthesis)

Abstract
This thesis extends the use of kernel learning techniques to specific problems of image classification. Kernel learning is a paradigm in the field of machine learning that generalizes the use of inner products to compute similarities between arbitrary objects. In image classification one aims to separate images based on their visual content. We address two important problems that arise in this context: learning with weak label information and combination of heterogeneous data sources. The contributions we report on are not unique to image classification, and apply to a more general class of problems. We study the problem of learning with label ambiguity in the multiple instance learning framework. We discuss several different image classification scenarios that arise in this context and argue that the standard multiple instance learning requires a more detailed disambiguation. Finally we review kernel learning approaches proposed for this problem and derive a more efficient algorithm to solve them. The multiple kernel learning framework is an approach to automatically select kernel parameters. We extend it to its infinite limit and present an algorithm to solve the resulting problem. This result is then applied in two directions. We show how to learn kernels that adapt to the special structure of images. Finally we compare different ways of combining image features for object classification and present significant improvements compared to previous methods.

PDF [BibTex]

PDF [BibTex]


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A PAC-Bayesian Approach to Structure Learning

Seldin, Y.

Biologische Kybernetik, The Hebrew University of Jerusalem, Israel, September 2009 (phdthesis)

PDF [BibTex]

PDF [BibTex]


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Expectation Propagation on the Maximum of Correlated Normal Variables

Hennig, P.

Cavendish Laboratory: University of Cambridge, July 2009 (techreport)

Abstract
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities.

Web [BibTex]

Web [BibTex]


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Consistent Nonparametric Tests of Independence

Gretton, A., Györfi, L.

(172), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2009 (techreport)

Abstract
Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when the empirical distribution of the variables is restricted to finite partitions. A third test statistic is defined as a kernel-based independence measure. Two kinds of tests are provided. Distribution-free strong consistent tests are derived on the basis of large deviation bounds on the test statistcs: these tests make almost surely no Type I or Type II error after a random sample size. Asymptotically alpha-level tests are obtained from the limiting distribution of the test statistics. For the latter tests, the Type I error converges to a fixed non-zero value alpha, and the Type II error drops to zero, for increasing sample size. All tests reject the null hypothesis of independence if the test statistics become large. The performance of the tests is evaluated experimentally on benchmark data.

PDF [BibTex]

PDF [BibTex]


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Randomized algorithms for statistical image analysis based on percolation theory

Davies, P., Langovoy, M., Wittich, O.

27th European Meeting of Statisticians (EMS), July 2009 (talk)

Abstract
We propose a novel probabilistic method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation and random graph theories (see Grimmett (1999)). We address the problem of detection and estimation of signals in situations where the signal-to-noise ratio is particularly low. We present an algorithm that allows to detect objects of various shapes in noisy images. The algorithm has linear complexity and exponential accuracy. Our algorithm substantially di ers from wavelets-based algorithms (see Arias-Castro et.al. (2005)). Moreover, we present an algorithm that produces a crude estimate of an object based on the noisy picture. This algorithm also has linear complexity and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedures.

Web PDF [BibTex]

Web PDF [BibTex]


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Learning Motor Primitives for Robotics

Kober, J., Peters, J., Oztop, E.

Advanced Telecommunications Research Center ATR, June 2009 (talk)

Abstract
The acquisition and self-improvement of novel motor skills is among the most important problems in robotics. Motor primitives offer one of the most promising frameworks for the application of machine learning techniques in this context. Employing the Dynamic Systems Motor primitives originally introduced by Ijspeert et al. (2003), appropriate learning algorithms for a concerted approach of both imitation and reinforcement learning are presented. Using these algorithms new motor skills, i.e., Ball-in-a-Cup, Ball-Paddling and Dart-Throwing, are learned.

[BibTex]

[BibTex]


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Learning To Detect Unseen Object Classes by Between-Class Attribute Transfer

Lampert, C.

IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 2009 (talk)

Web [BibTex]

Web [BibTex]


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Semi-supervised subspace analysis of human functional magnetic resonance imaging data

Shelton, J., Blaschko, M., Bartels, A.

(185), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2009 (techreport)

Abstract
Kernel Canonical Correlation Analysis is a very general technique for subspace learning that incorporates PCA and LDA as special cases. Functional magnetic resonance imaging (fMRI) acquired data is naturally amenable to these techniques as data are well aligned. fMRI data of the human brain is a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single- and multi-variate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, the semi-supervised variants of KCCA performed better than the supervised variants, including a supervised variant with Laplacian regularization. We additionally analyze the weights learned by the regression in order to infer brain regions that are important to different types of visual processing.

PDF [BibTex]

PDF [BibTex]


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Kernel Methods in Computer Vision:Object Localization, Clustering,and Taxonomy Discovery

Blaschko, MB.

Biologische Kybernetik, Technische Universität Berlin, Berlin, Germany, March 2009 (phdthesis)

PDF PDF [BibTex]

PDF PDF [BibTex]


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Model selection, large deviations and consistency of data-driven tests

Langovoy, M.

(2009-007), EURANDOM, Technische Universiteit Eindhoven, March 2009 (techreport)

Abstract
We consider three general classes of data-driven statistical tests. Neyman's smooth tests, data-driven score tests and data-driven score tests for statistical inverse problems serve as important special examples for the classes of tests under consideration. Our tests are additionally incorporated with model selection rules. The rules are based on the penalization idea. Most of the optimal penalties, derived in statistical literature, can be used in our tests. We prove general consistency theorems for the tests from those classes. Our proofs make use of large deviations inequalities for deterministic and random quadratic forms. The paper shows that the tests can be applied for simple and composite parametric, semi- and nonparametric hypotheses. Applications to testing in statistical inverse problems and statistics for stochastic processes are also presented..

PDF [BibTex]

PDF [BibTex]


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Motor Control and Learning in Table Tennis

Mülling, K.

Eberhard Karls Universität Tübingen, Gerrmany, 2009 (diplomathesis)

[BibTex]

[BibTex]


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Hierarchical Clustering and Density Estimation Based on k-nearest-neighbor graphs

Drewe, P.

Eberhard Karls Universität Tübingen, Germany, 2009 (diplomathesis)

[BibTex]

[BibTex]


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Learning with Structured Data: Applications to Computer Vision

Nowozin, S.

Technische Universität Berlin, Germany, 2009 (phdthesis)

PDF [BibTex]

PDF [BibTex]

2004


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Fast Binary and Multi-Output Reduced Set Selection

Weston, J., Bakir, G.

(132), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2004 (techreport)

Abstract
We propose fast algorithms for reducing the number of kernel evaluations in the testing phase for methods such as Support Vector Machines (SVM) and Ridge Regression (RR). For non-sparse methods such as RR this results in significantly improved prediction time. For binary SVMs, which are already sparse in their expansion, the pay off is mainly in the cases of noisy or large-scale problems. However, we then further develop our method for multi-class problems where, after choosing the expansion to find vectors which describe all the hyperplanes jointly, we again achieve significant gains.

PostScript [BibTex]

2004

PostScript [BibTex]


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Joint Kernel Maps

Weston, J., Schölkopf, B., Bousquet, O., Mann, .., Noble, W.

(131), Max-Planck-Institute for Biological Cybernetics, Tübingen, November 2004 (techreport)

PDF [BibTex]

PDF [BibTex]


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Discrete vs. Continuous: Two Sides of Machine Learning

Zhou, D.

October 2004 (talk)

Abstract
We consider the problem of transductive inference. In many real-world problems, unlabeled data is far easier to obtain than labeled data. Hence transductive inference is very significant in many practical problems. According to Vapnik's point of view, one should predict the function value only on the given points directly rather than a function defined on the whole space, the latter being a more complicated problem. Inspired by this idea, we develop discrete calculus on finite discrete spaces, and then build discrete regularization. A family of transductive algorithms is naturally derived from this regularization framework. We validate the algorithms on both synthetic and real-world data from text/web categorization to bioinformatics problems. A significant by-product of this work is a powerful way of ranking data based on examples including images, documents, proteins and many other kinds of data. This talk is mainly based on the followiing contribution: (1) D. Zhou and B. Sch{\"o}lkopf: Transductive Inference with Graphs, MPI Technical report, August, 2004; (2) D. Zhou, B. Sch{\"o}lkopf and T. Hofmann. Semi-supervised Learning on Directed Graphs. NIPS 2004; (3) D. Zhou, O. Bousquet, T.N. Lal, J. Weston and B. Sch{\"o}lkopf. Learning with Local and Global Consistency. NIPS 2003.

PDF [BibTex]


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Independent component analysis and beyond

Harmeling, S.

Biologische Kybernetik, Universität Potsdam, Potsdam, October 2004 (phdthesis)

PDF [BibTex]

PDF [BibTex]


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Grundlagen von Support Vector Maschinen und Anwendungen in der Bildverarbeitung

Eichhorn, J.

September 2004 (talk)

Abstract
Invited talk at the workshop "Numerical, Statistical and Discrete Methods in Image Processing" at the TU M{\"u}nchen (in GERMAN)

PDF [BibTex]


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Semi-Supervised Induction

Yu, K., Tresp, V., Zhou, D.

(141), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, August 2004 (techreport)

Abstract
Considerable progress was recently achieved on semi-supervised learning, which differs from the traditional supervised learning by additionally exploring the information of the unlabelled examples. However, a disadvantage of many existing methods is that it does not generalize to unseen inputs. This paper investigates learning methods that effectively make use of both labelled and unlabelled data to build predictive functions, which are defined on not just the seen inputs but the whole space. As a nice property, the proposed method allows effcient training and can easily handle new test points. We validate the method based on both toy data and real world data sets.

PDF PDF [BibTex]

PDF PDF [BibTex]


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On Hausdorff Distance Measures

Shapiro, MD., Blaschko, MB.

Department of Computer Science, University of Massachusetts Amherst, August 2004 (techreport)

[BibTex]

[BibTex]


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The benefit of liquid Helium cooling for Cryo-Electron Tomography: A quantitative comparative study

Schweikert, G., Luecken, U., Pfeifer, G., Baumeister, W., Plitzko, J.

The thirteenth European Microscopy Congress, August 2004 (talk)

[BibTex]

[BibTex]


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Object categorization with SVM: kernels for local features

Eichhorn, J., Chapelle, O.

(137), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2004 (techreport)

Abstract
In this paper, we propose to combine an efficient image representation based on local descriptors with a Support Vector Machine classifier in order to perform object categorization. For this purpose, we apply kernels defined on sets of vectors. After testing different combinations of kernel / local descriptors, we have been able to identify a very performant one.

PDF [BibTex]

PDF [BibTex]


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Hilbertian Metrics and Positive Definite Kernels on Probability Measures

Hein, M., Bousquet, O.

(126), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2004 (techreport)

Abstract
We investigate the problem of defining Hilbertian metrics resp. positive definite kernels on probability measures, continuing previous work. This type of kernels has shown very good results in text classification and has a wide range of possible applications. In this paper we extend the two-parameter family of Hilbertian metrics of Topsoe such that it now includes all commonly used Hilbertian metrics on probability measures. This allows us to do model selection among these metrics in an elegant and unified way. Second we investigate further our approach to incorporate similarity information of the probability space into the kernel. The analysis provides a better understanding of these kernels and gives in some cases a more efficient way to compute them. Finally we compare all proposed kernels in two text and one image classification problem.

PDF [BibTex]

PDF [BibTex]


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Kernels, Associated Structures and Generalizations

Hein, M., Bousquet, O.

(127), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2004 (techreport)

Abstract
This paper gives a survey of results in the mathematical literature on positive definite kernels and their associated structures. We concentrate on properties which seem potentially relevant for Machine Learning and try to clarify some results that have been misused in the literature. Moreover we consider different lines of generalizations of positive definite kernels. Namely we deal with operator-valued kernels and present the general framework of Hilbertian subspaces of Schwartz which we use to introduce kernels which are distributions. Finally indefinite kernels and their associated reproducing kernel spaces are considered.

PDF [BibTex]

PDF [BibTex]


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Riemannian Geometry on Graphs and its Application to Ranking and Classification

Zhou, D.

June 2004 (talk)

Abstract
We consider the problem of transductive inference. In many real-world problems, unlabeled data is far easier to obtain than labeled data. Hence transductive inference is very significant in many practical problems. According to Vapnik's point of view, one should predict the function value only on the given points directly rather than a function defined on the whole space, the latter being a more complicated problem. Inspired by this idea, we develop discrete calculus on finite discrete spaces, and then build discrete regularization. A family of transductive algorithms is naturally derived from this regularization framework. We validate the algorithms on both synthetic and real-world data from text/web categorization to bioinformatics problems. A significant by-product of this work is a powerful way of ranking data based on examples including images, documents, proteins and many other kinds of data.

PDF [BibTex]


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Triangle Fixing Algorithms for the Metric Nearness Problem

Dhillon, I., Sra, S., Tropp, J.

Univ. of Texas at Austin, June 2004 (techreport)

PDF [BibTex]

PDF [BibTex]


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Exploration of combining Echo-State Network Learning with Recurrent Neural Network Learning techniques

Erhan, D.

Biologische Kybernetik, International University Bremen, Bremen, Germany, May 2004 (diplomathesis)

PDF [BibTex]

PDF [BibTex]


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Kamerakalibrierung und Tiefenschätzung: Ein Vergleich von klassischer Bündelblockausgleichung und statistischen Lernalgorithmen

Sinz, FH.

Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Germany, March 2004 (techreport)

Abstract
Die Arbeit verleicht zwei Herangehensweisen an das Problem der Sch{\"a}tzung der r{\"a}umliche Position eines Punktes aus den Bildkoordinaten in zwei verschiedenen Kameras. Die klassische Methode der B{\"u}ndelblockausgleichung modelliert zwei Einzelkameras und sch{\"a}tzt deren {\"a}ußere und innere Orientierung mit einer iterativen Kalibrationsmethode, deren Konvergenz sehr stark von guten Startwerten abh{\"a}ngt. Die Tiefensch{\"a}tzung eines Punkts geschieht durch die Invertierung von drei der insgesamt vier Projektionsgleichungen der Einzalkameramodelle. Die zweite Methode benutzt Kernel Ridge Regression und Support Vector Regression, um direkt eine Abbildung von den Bild- auf die Raumkoordinaten zu lernen. Die Resultate zeigen, daß der Ansatz mit maschinellem Lernen, neben einer erheblichen Vereinfachung des Kalibrationsprozesses, zu h{\"o}heren Positionsgenaugikeiten f{\"u}hren kann.

PDF [BibTex]

PDF [BibTex]


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Computational Analysis of Gene Expression Data

Zien, A.

(4), Biologische Kybernetik, March 2004 (phdthesis)

[BibTex]

[BibTex]


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Learning from Labeled and Unlabeled Data: Semi-supervised Learning and Ranking

Zhou, D.

January 2004 (talk)

Abstract
We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data.

PDF [BibTex]


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Introduction to Category Theory

Bousquet, O.

Internal Seminar, January 2004 (talk)

Abstract
A brief introduction to the general idea behind category theory with some basic definitions and examples. A perspective on higher dimensional categories is given.

PDF [BibTex]

PDF [BibTex]


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Multivariate Regression with Stiefel Constraints

Bakir, G., Gretton, A., Franz, M., Schölkopf, B.

(128), MPI for Biological Cybernetics, Spemannstr 38, 72076, Tuebingen, 2004 (techreport)

Abstract
We introduce a new framework for regression between multi-dimensional spaces. Standard methods for solving this problem typically reduce the problem to one-dimensional regression by choosing features in the input and/or output spaces. These methods, which include PLS (partial least squares), KDE (kernel dependency estimation), and PCR (principal component regression), select features based on different a-priori judgments as to their relevance. Moreover, loss function and constraints are chosen not primarily on statistical grounds, but to simplify the resulting optimisation. By contrast, in our approach the feature construction and the regression estimation are performed jointly, directly minimizing a loss function that we specify, subject to a rank constraint. A major advantage of this approach is that the loss is no longer chosen according to the algorithmic requirements, but can be tailored to the characteristics of the task at hand; the features will then be optimal with respect to this objective. Our approach also allows for the possibility of using a regularizer in the optimization. Finally, by processing the observations sequentially, our algorithm is able to work on large scale problems.

PDF [BibTex]

PDF [BibTex]


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The p53 Oligomerization Domain: Sequence-Structure Relationships and the Design and Characterization of Altered Oligomeric States

Davison, TS.

University of Toronto, Canada, University of Toronto, Canada, 2004 (phdthesis)

[BibTex]

[BibTex]


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Learning from Labeled and Unlabeled Data Using Random Walks

Zhou, D., Schölkopf, B.

Max Planck Institute for Biological Cybernetics, 2004 (techreport)

Abstract
We consider the general problem of learning from labeled and unlabeled data. Given a set of points, some of them are labeled, and the remaining points are unlabeled. The goal is to predict the labels of the unlabeled points. Any supervised learning algorithm can be applied to this problem, for instance, Support Vector Machines (SVMs). The problem of our interest is if we can implement a classifier which uses the unlabeled data information in some way and has higher accuracy than the classifiers which use the labeled data only. Recently we proposed a simple algorithm, which can substantially benefit from large amounts of unlabeled data and demonstrates clear superiority to supervised learning methods. In this paper we further investigate the algorithm using random walks and spectral graph theory, which shed light on the key steps in this algorithm.

PDF PostScript [BibTex]

PDF PostScript [BibTex]


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Behaviour and Convergence of the Constrained Covariance

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

(130), MPI for Biological Cybernetics, 2004 (techreport)

Abstract
We discuss reproducing kernel Hilbert space (RKHS)-based measures of statistical dependence, with emphasis on constrained covariance (COCO), a novel criterion to test dependence of random variables. We show that COCO is a test for independence if and only if the associated RKHSs are universal. That said, no independence test exists that can distinguish dependent and independent random variables in all circumstances. Dependent random variables can result in a COCO which is arbitrarily close to zero when the source densities are highly non-smooth, which can make dependence hard to detect empirically. All current kernel-based independence tests share this behaviour. Finally, we demonstrate exponential convergence between the population and empirical COCO, which implies that COCO does not suffer from slow learning rates when used as a dependence test.

PDF [BibTex]

PDF [BibTex]


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Statistical Learning with Similarity and Dissimilarity Functions

von Luxburg, U.

pages: 1-166, Technische Universität Berlin, Germany, Technische Universität Berlin, Germany, 2004 (phdthesis)

PDF PostScript [BibTex]

PDF PostScript [BibTex]