Publications | Max Planck Institute for Intelligent Systems

2016

am ics Ebner, S., Trimpe, S. Supplemental material for ’Communication Rate Analysis for Event-based State Estimation’ Max Planck Institute for Intelligent Systems, January 2016 (techreport)

2015

Distributed Event-based State Estimation

Trimpe, S.

Max Planck Institute for Intelligent Systems, November 2015 (techreport)

Abstract

An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor-actuator-agents observe a dynamic process and sporadically exchange their measurements and inputs over a bus network. Based on these data, each agent estimates the full state of the dynamic system, which may exhibit arbitrary inter-agent couplings. Local event-based protocols ensure that data is transmitted only when necessary to meet a desired estimation accuracy. This event-based scheme is shown to mimic a centralized Luenberger observer design up to guaranteed bounds, and stability is proven in the sense of bounded estimation errors for bounded disturbances. The stability result extends to the distributed control system that results when the local state estimates are used for distributed feedback control. Simulation results highlight the benefit of the event-based approach over classical periodic ones in reducing communication requirements.

am ics

arXiv [BibTex]

2015

am ics Trimpe, S. Distributed Event-based State Estimation Max Planck Institute for Intelligent Systems, November 2015 (techreport)

arXiv [BibTex]

Cosmology from Cosmic Shear with DES Science Verification Data

Abbott, T., Abdalla, F. B., Allam, S., Amara, A., Annis, J., Armstrong, R., Bacon, D., Banerji, M., Bauer, A. H., Baxter, E., others,

arXiv preprint arXiv:1507.05552, 2015 (techreport)

ei Abbott, T., Abdalla, F. B., Allam, S., Amara, A., Annis, J., Armstrong, R., Bacon, D., Banerji, M., Bauer, A. H., Baxter, E., others, Cosmology from Cosmic Shear with DES Science Verification Data arXiv preprint arXiv:1507.05552, 2015 (techreport)

The DES Science Verification Weak Lensing Shear Catalogs

Jarvis, M., Sheldon, E., Zuntz, J., Kacprzak, T., Bridle, S. L., Amara, A., Armstrong, R., Becker, M. R., Bernstein, G. M., Bonnett, C., others,

arXiv preprint arXiv:1507.05603, 2015 (techreport)

ei Jarvis, M., Sheldon, E., Zuntz, J., Kacprzak, T., Bridle, S. L., Amara, A., Armstrong, R., Becker, M. R., Bernstein, G. M., Bonnett, C., others, The DES Science Verification Weak Lensing Shear Catalogs arXiv preprint arXiv:1507.05603, 2015 (techreport)

2007

Bayesian Estimators for Robins-Ritovs Problem

Harmeling, S., Toussaint, M.

(EDI-INF-RR-1189), School of Informatics, University of Edinburgh, October 2007 (techreport)

Abstract

Bayesian or likelihood-based approaches to data analysis became very popular in the ﬁeld of Machine Learning. However, there exist theoretical results which question the general applicability of such approaches; among those a result by Robins and Ritov which introduce a speciﬁc example for which they prove that a likelihood-based estimator will fail (i.e. it does for certain cases not converge to a true parameter estimate, even given inﬁnite data). In this paper we consider various approaches to formulate likelihood-based estimators in this example, basically by considering various extensions of the presumed generative model of the data. We can derive estimators which are very similar to the classical Horvitz-Thompson and which also account for a priori knowledge of an observation probability function.

2007

ei Harmeling, S., Toussaint, M. Bayesian Estimators for Robins-Ritovs Problem (EDI-INF-RR-1189), School of Informatics, University of Edinburgh, October 2007 (techreport)

Learning with Transformation Invariant Kernels

Walder, C., Chapelle, O.

(165), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2007 (techreport)

Abstract

Abstract. This paper considers kernels invariant to translation, rotation and dilation. We show that no non-trivial positive definite (p.d.) kernels exist which are radial and dilation invariant, only conditionally positive definite (c.p.d.) ones. Accordingly, we discuss the c.p.d. case and provide some novel analysis, including an elementary derivation of a c.p.d. representer theorem. On the practical side, we give a support vector machine (s.v.m.) algorithm for arbitrary c.p.d. kernels. For the thin-plate kernel this leads to a classifier with only one parameter (the amount of regularisation), which we demonstrate to be as effective as an s.v.m. with the Gaussian kernel, even though the Gaussian involves a second parameter (the length scale).

ei Walder, C., Chapelle, O. Learning with Transformation Invariant Kernels (165), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2007 (techreport)

Scalable Semidefinite Programming using Convex Perturbations

Kulis, B., Sra, S., Jegelka, S.

(TR-07-47), University of Texas, Austin, TX, USA, September 2007 (techreport)

Abstract

Several important machine learning problems can be modeled and solved via semidefinite programs. Often, researchers invoke off-the-shelf software for the associated optimization, which can be inappropriate for many applications due to computational and storage requirements. In this paper, we introduce the use of convex perturbations for semidefinite programs (SDPs). Using a particular perturbation function, we arrive at an algorithm for SDPs that has several advantages over existing techniques: a) it is simple, requiring only a few lines of MATLAB, b) it is a first-order method which makes it scalable, c) it can easily exploit the structure of a particular SDP to gain efficiency (e.g., when the constraint matrices are low-rank). We demonstrate on several machine learning applications that the proposed algorithm is effective in finding fast approximations to large-scale SDPs.

ei Kulis, B., Sra, S., Jegelka, S. Scalable Semidefinite Programming using Convex Perturbations (TR-07-47), University of Texas, Austin, TX, USA, September 2007 (techreport)

Sparse Multiscale Gaussian Process Regression

Walder, C., Kim, K., Schölkopf, B.

(162), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2007 (techreport)

Abstract

Most existing sparse Gaussian process (g.p.) models seek computational advantages by basing their computations on a set of m basis functions that are the covariance function of the g.p. with one of its two inputs fixed. We generalise this for the case of Gaussian covariance function, by basing our computations on m Gaussian basis functions with arbitrary diagonal covariance matrices (or length scales). For a fixed number of basis functions and any given criteria, this additional flexibility permits approximations no worse and typically better than was previously possible. Although we focus on g.p. regression, the central idea is applicable to all kernel based algorithms, such as the support vector machine. We perform gradient based optimisation of the marginal likelihood, which costs O(m2n) time where n is the number of data points, and compare the method to various other sparse g.p. methods. Our approach outperforms the other methods, particularly for the case of very few basis functions, i.e. a very high sparsity ratio.

ei Walder, C., Kim, K., Schölkopf, B. Sparse Multiscale Gaussian Process Regression (162), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2007 (techreport)

Efficient Subwindow Search for Object Localization

Blaschko, M., Hofmann, T., Lampert, C.

(164), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2007 (techreport)

Abstract

Recent years have seen huge advances in object recognition from images. Recognition rates beyond 95% are the rule rather than the exception on many datasets. However, most state-of-the-art methods can only decide if an object is present or not. They are not able to provide information on the object location or extent within in the image. We report on a simple yet powerful scheme that extends many existing recognition methods to also perform localization of object bounding boxes. This is achieved by maximizing the classification score over all possible subrectangles in the image. Despite the impression that this would be computationally intractable, we show that in many situations efficient algorithms exist which solve a generalized maximum subrectangle problem. We show how our method is applicable to a variety object detection frameworks and demonstrate its performance by applying it to the popular bag of visual words model, achieving competitive results on the PASCAL VOC 2006 dataset.

ei Blaschko, M., Hofmann, T., Lampert, C. Efficient Subwindow Search for Object Localization (164), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2007 (techreport)

Cluster Identification in Nearest-Neighbor Graphs

Maier, M., Hein, M., von Luxburg, U.

(163), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, May 2007 (techreport)

Abstract

Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are ``identified‘‘: that is, the subgraph induced by points from the same cluster is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds on the probability that cluster identification is successful, and use them to predict ``optimal‘‘ values of k for the mutual and symmetric k-nearest-neighbor graphs. We point out different properties of the mutual and symmetric nearest-neighbor graphs related to the cluster identification problem.

ei Maier, M., Hein, M., von Luxburg, U. Cluster Identification in Nearest-Neighbor Graphs (163), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, May 2007 (techreport)

Exploring model selection techniques for nonlinear dimensionality reduction

Harmeling, S.

(EDI-INF-RR-0960), School of Informatics, University of Edinburgh, March 2007 (techreport)

Abstract

Nonlinear dimensionality reduction (NLDR) methods have become useful tools for practitioners who are faced with the analysis of high-dimensional data. Of course, not all NLDR methods are equally applicable to a particular dataset at hand. Thus it would be useful to come up with model selection criteria that help to choose among diﬀerent NLDR algorithms. This paper explores various approaches to this problem and evaluates them on controlled data sets. Comprehensive experiments will show that model selection scores based on stability are not useful, while scores based on Gaussian processes are helpful for the NLDR problem.

ei Harmeling, S. Exploring model selection techniques for nonlinear dimensionality reduction (EDI-INF-RR-0960), School of Informatics, University of Edinburgh, March 2007 (techreport)

Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach

Chiappa, S., Barber, D.

(161), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, March 2007 (techreport)

Abstract

We describe two related models to cluster multidimensional time-series under the assumption of an underlying linear Gaussian dynamical process. In the first model, times-series are assigned to the same cluster when they show global similarity in their dynamics, while in the second model times-series are assigned to the same cluster when they show simultaneous similarity. Both models are based on Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models in order to (semi) automatically determine an appropriate number of components in the mixture, and to additionally bias the components to a parsimonious parameterization. The resulting models are formally intractable and to deal with this we describe a deterministic approximation based on a novel implementation of Variational Bayes.

ei Chiappa, S., Barber, D. Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach (161), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, March 2007 (techreport)

Modeling data using directional distributions: Part II

Sra, S., Jain, P., Dhillon, I.

(TR-07-05), University of Texas, Austin, TX, USA, February 2007 (techreport)

Abstract

High-dimensional data is central to most data mining applications, and only recently has it been modeled via directional distributions. In [Banerjee et al., 2003] the authors introduced the use of the von Mises-Fisher (vMF) distribution for modeling high-dimensional directional data, particularly for text and gene expression analysis. The vMF distribution is one of the simplest directional distributions. TheWatson, Bingham, and Fisher-Bingham distributions provide distri- butions with an increasing number of parameters and thereby commensurately increased modeling power. This report provides a followup study to the initial development in [Banerjee et al., 2003] by presenting Expectation Maximization (EM) procedures for estimating parameters of a mixture of Watson (moW) distributions. The numerical challenges associated with parameter estimation for both of these distributions are significantly more difficult than for the vMF distribution. We develop new numerical approximations for estimating the parameters permitting us to model real- life data more accurately. Our experimental results establish that for certain data sets improved modeling power translates into better results.

ei Sra, S., Jain, P., Dhillon, I. Modeling data using directional distributions: Part II (TR-07-05), University of Texas, Austin, TX, USA, February 2007 (techreport)

Automatic 3D Face Reconstruction from Single Images or Video

Breuer, P., Kim, K., Kienzle, W., Blanz, V., Schölkopf, B.

(160), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, February 2007 (techreport)

Abstract

This paper presents a fully automated algorithm for reconstructing a textured 3D model of a face from a single photograph or a raw video stream. The algorithm is based on a combination of Support Vector Machines (SVMs) and a Morphable Model of 3D faces. After SVM face detection, individual facial features are detected using a novel regression-and classification-based approach, and probabilistically plausible configurations of features are selected to produce a list of candidates for several facial feature positions. In the next step, the configurations of feature points are evaluated using a novel criterion that is based on a Morphable Model and a combination of linear projections. Finally, the feature points initialize a model-fitting procedure of the Morphable Model. The result is a high-resolution 3D surface model.

ei Breuer, P., Kim, K., Kienzle, W., Blanz, V., Schölkopf, B. Automatic 3D Face Reconstruction from Single Images or Video (160), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, February 2007 (techreport)

Relative Entropy Policy Search

Peters, J.

CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

Abstract

This technical report describes a cute idea of how to create new policy search approaches. It directly relates to the Natural Actor-Critic methods but allows the derivation of one shot solutions. Future work may include the application to interesting problems.

am ei

PDF link (url) [BibTex]

am ei Peters, J. Relative Entropy Policy Search CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

PDF link (url) [BibTex]

Denoising archival films using a learned Bayesian model

Moldovan, T. M., Roth, S., Black, M. J.

(CS-07-03), Brown University, Department of Computer Science, 2007 (techreport)

pdf [BibTex]

ps Moldovan, T. M., Roth, S., Black, M. J. Denoising archival films using a learned Bayesian model (CS-07-03), Brown University, Department of Computer Science, 2007 (techreport)

pdf [BibTex]

Learning an Outlier-Robust Kalman Filter

Ting, J., Theodorou, E., Schaal, S.

CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

Abstract

We introduce a modified Kalman filter that performs robust, real-time outlier detection, without the need for manual parameter tuning by the user. Systems that rely on high quality sensory data (for instance, robotic systems) can be sensitive to data containing outliers. The standard Kalman filter is not robust to outliers, and other variations of the Kalman filter have been proposed to overcome this issue. However, these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation procedures. Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample. A data sample with a smaller weight has a weaker contribution when estimating the current time step?s state. Using an incremental variational Expectation-Maximization framework, we learn the weights and system dynamics. We evaluate our Kalman filter algorithm on data from a robotic dog.

am Ting, J., Theodorou, E., Schaal, S. Learning an Outlier-Robust Kalman Filter CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

2004

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.

2004

ei Weston, J., Bakir, G. Fast Binary and Multi-Output Reduced Set Selection (132), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2004 (techreport)

Joint Kernel Maps

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

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

ei Weston, J., Schölkopf, B., Bousquet, O., Mann, .., Noble, W. Joint Kernel Maps (131), Max-Planck-Institute for Biological Cybernetics, Tübingen, November 2004 (techreport)

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]

ei Yu, K., Tresp, V., Zhou, D. Semi-Supervised Induction (141), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, August 2004 (techreport)

PDF PDF [BibTex]

On Hausdorff Distance Measures

Shapiro, MD., Blaschko, MB.

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

ei Shapiro, MD., Blaschko, MB. On Hausdorff Distance Measures Department of Computer Science, University of Massachusetts Amherst, August 2004 (techreport)

Eichhorn, J., Chapelle, O.

Object categorization with SVM: kernels for local features

(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.

ei Eichhorn, J., Chapelle, O. Object categorization with SVM: kernels for local features (137), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2004 (techreport)

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.

ei Hein, M., Bousquet, O. Hilbertian Metrics and Positive Definite Kernels on Probability Measures (126), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2004 (techreport)

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.

ei Hein, M., Bousquet, O. Kernels, Associated Structures and Generalizations (127), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2004 (techreport)

Triangle Fixing Algorithms for the Metric Nearness Problem

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

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

ei Dhillon, I., Sra, S., Tropp, J. Triangle Fixing Algorithms for the Metric Nearness Problem Univ. of Texas at Austin, June 2004 (techreport)

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.

ei Sinz, FH. Kamerakalibrierung und Tiefenschätzung: Ein Vergleich von klassischer Bündelblockausgleichung und statistischen Lernalgorithmen Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Germany, March 2004 (techreport)

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.

ei Bakir, G., Gretton, A., Franz, M., Schölkopf, B. Multivariate Regression with Stiefel Constraints (128), MPI for Biological Cybernetics, Spemannstr 38, 72076, Tuebingen, 2004 (techreport)

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]

ei Zhou, D., Schölkopf, B. Learning from Labeled and Unlabeled Data Using Random Walks Max Planck Institute for Biological Cybernetics, 2004 (techreport)

PDF PostScript [BibTex]

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.

ei Gretton, A., Smola, A., Bousquet, O., Herbrich, R., Schölkopf, B., Logothetis, N. Behaviour and Convergence of the Constrained Covariance (130), MPI for Biological Cybernetics, 2004 (techreport)

Confidence Sets for Ratios: A Purely Geometric Approach To Fieller’s Theorem

von Luxburg, U., Franz, V.

(133), Max Planck Institute for Biological Cybernetics, 2004 (techreport)

Abstract

We present a simple, geometric method to construct Fieller's exact confidence sets for ratios of jointly normally distributed random variables. Contrary to previous geometric approaches in the literature, our method is valid in the general case where both sample mean and covariance are unknown. Moreover, not only the construction but also its proof are purely geometric and elementary, thus giving intuition into the nature of the confidence sets.

ei von Luxburg, U., Franz, V. Confidence Sets for Ratios: A Purely Geometric Approach To Fieller’s Theorem (133), Max Planck Institute for Biological Cybernetics, 2004 (techreport)

Transductive Inference with Graphs

Zhou, D., Schölkopf, B.

Max Planck Institute for Biological Cybernetics, 2004, See the improved version Regularization on Discrete Spaces. (techreport)

Abstract

We propose a general regularization framework for transductive inference. The given data are thought of as a graph, where the edges encode the pairwise relationships among data. We develop discrete analysis and geometry on graphs, and then naturally adapt the classical regularization in the continuous case to the graph situation. A new and effective algorithm is derived from this general framework, as well as an approach we developed before.

ei Zhou, D., Schölkopf, B. Transductive Inference with Graphs Max Planck Institute for Biological Cybernetics, 2004, See the improved version Regularization on Discrete Spaces. (techreport)

Kompetenzerwerb für Informationssysteme - Einfluss des Lernprozesses auf die Interaktion mit Fahrerinformationssystemen. Veröffentlichter Abschlussbericht (Förderkennzeichen BaSt FE 82.196/2001).

Totzke, I., Krüger, H., Hofmann, M., Meilinger, T., Rauch, N., Schmidt, G.

Interdisziplinäres Zentrum für Verkehrswissenschaften (IZVW), Würzburg, 2004 (techreport)

ei Totzke, I., Krüger, H., Hofmann, M., Meilinger, T., Rauch, N., Schmidt, G. Kompetenzerwerb für Informationssysteme - Einfluss des Lernprozesses auf die Interaktion mit Fahrerinformationssystemen. Veröffentlichter Abschlussbericht (Förderkennzeichen BaSt FE 82.196/2001). Interdisziplinäres Zentrum für Verkehrswissenschaften (IZVW), Würzburg, 2004 (techreport)

2001

Kernel Methods for Extracting Local Image Semantics

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

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

2001

ei Bradshaw, B., Schölkopf, B., Platt, J. Kernel Methods for Extracting Local Image Semantics (MSR-TR-2001-99), Microsoft Research, October 2001 (techreport)

Calibration of Digital Amateur Cameras

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

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

ei Urbanek, M., Horaud, R., Sturm, P. Calibration of Digital Amateur Cameras (RR-4214), INRIA Rhone Alpes, Montbonnot, France, July 2001 (techreport)

Weston, J., Elisseeff, A., Schölkopf, B.

Use of the ell_0-norm with linear models and kernel methods

Biowulf Technologies, 2001 (techreport)

ei Weston, J., Elisseeff, A., Schölkopf, B. Use of the ell_0-norm with linear models and kernel methods Biowulf Technologies, 2001 (techreport)

KDD Cup 2001 data analysis: prediction of molecular bioactivity for drug design – Binding to Thrombin

Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B.

BIOwulf, 2001 (techreport)

ei Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B. KDD Cup 2001 data analysis: prediction of molecular bioactivity for drug design – Binding to Thrombin BIOwulf, 2001 (techreport)

Chapelle, O., Schölkopf, B.

Incorporating Invariances in Non-Linear Support Vector Machines

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.

ei Chapelle, O., Schölkopf, B. Incorporating Invariances in Non-Linear Support Vector Machines Max Planck Institute for Biological Cybernetics / Biowulf Technologies, 2001 (techreport)

Data cleaning algorithms with applications to micro-array experiments

Weston, J., Chapelle, O., Guyon, I.

Biowulf, 2001 (techreport)

ei Weston, J., Chapelle, O., Guyon, I. Data cleaning algorithms with applications to micro-array experiments Biowulf, 2001 (techreport)

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)

ei Gretton, A., Herbrich, R., Schölkopf, B., Smola, A., Rayner, P. Bound on the Leave-One-Out Error for Density Support Estimation using nu-SVMs University of Cambridge, 2001 (techreport)

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.

ei Gretton, A., Herbrich, R., Schölkopf, B., Rayner, P. Bound on the Leave-One-Out Error for 2-Class Classification using nu-SVMs University of Cambridge, 2001, Updated May 2003 (literature review expanded) (techreport)

Some kernels for structured data

Bartlett, P., Schölkopf, B.

Biowulf Technologies, 2001 (techreport)

ei Bartlett, P., Schölkopf, B. Some kernels for structured data Biowulf Technologies, 2001 (techreport)

Inference Principles and Model Selection

Buhmann, J., Schölkopf, B.

(01301), Dagstuhl Seminar, 2001 (techreport)

ei Buhmann, J., Schölkopf, B. Inference Principles and Model Selection (01301), Dagstuhl Seminar, 2001 (techreport)

2000

The Kernel Trick for Distances

Schölkopf, B.

(MSR-TR-2000-51), Microsoft Research, Redmond, WA, USA, 2000 (techreport)

Abstract

A method is described which, like the kernel trick in support vector machines (SVMs), lets us generalize distance-based algorithms to operate in feature spaces, usually nonlinearly related to the input space. This is done by identifying a class of kernels which can be represented as normbased distances in Hilbert spaces. It turns out that common kernel algorithms, such as SVMs and kernel PCA, are actually really distance based algorithms and can be run with that class of kernels, too. As well as providing a useful new insight into how these algorithms work, the present work can form the basis for conceiving new algorithms.

2000

ei Schölkopf, B. The Kernel Trick for Distances (MSR-TR-2000-51), Microsoft Research, Redmond, WA, USA, 2000 (techreport)

Kernel method for percentile feature extraction

Schölkopf, B., Platt, J., Smola, A.

(MSR-TR-2000-22), Microsoft Research, 2000 (techreport)

Abstract

A method is proposed which computes a direction in a dataset such that a speci􏰘ed fraction of a particular class of all examples is separated from the overall mean by a maximal margin􏰤 The pro jector onto that direction can be used for class􏰣speci􏰘c feature extraction􏰤 The algorithm is carried out in a feature space associated with a support vector kernel function􏰢 hence it can be used to construct a large class of nonlinear fea􏰣 ture extractors􏰤 In the particular case where there exists only one class􏰢 the method can be thought of as a robust form of principal component analysis􏰢 where instead of variance we maximize percentile thresholds􏰤 Fi􏰣 nally􏰢 we generalize it to also include the possibility of specifying negative examples􏰤

ei Schölkopf, B., Platt, J., Smola, A. Kernel method for percentile feature extraction (MSR-TR-2000-22), Microsoft Research, 2000 (techreport)