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25 results (View BibTeX file of all listed publications)

2007

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Bayesian Estimators for Robins-Ritov’s 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.

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2007

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

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Predicting Structured Data

Bakir, G., Hofmann, T., Schölkopf, B., Smola, A., Taskar, B., Vishwanathan, S.

pages: 360, Advances in neural information processing systems, MIT Press, Cambridge, MA, USA, September 2007 (book)

Abstract
Machine learning develops intelligent computer systems that are able to generalize from previously seen examples. A new domain of machine learning, in which the prediction must satisfy the additional constraints found in structured data, poses one of machine learning’s greatest challenges: learning functional dependencies between arbitrary input and output domains. This volume presents and analyzes the state of the art in machine learning algorithms and theory in this novel field. The contributors discuss applications as diverse as machine translation, document markup, computational biology, and information extraction, among others, providing a timely overview of an exciting field.

Web [BibTex]

Bakir, G., Hofmann, T., Schölkopf, B., Smola, A., Taskar, B., Vishwanathan, S. Predicting Structured Data pages: 360, Advances in neural information processing systems, MIT Press, Cambridge, MA, USA, September 2007 (book)

Web [BibTex]

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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).

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

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Large-Scale Kernel Machines

Bottou, L., Chapelle, O., DeCoste, D., Weston, J.

pages: 416, Neural Information Processing Series, MIT Press, Cambridge, MA, USA, September 2007 (book)

Abstract
Pervasive and networked computers have dramatically reduced the cost of collecting and distributing large datasets. In this context, machine learning algorithms that scale poorly could simply become irrelevant. We need learning algorithms that scale linearly with the volume of the data while maintaining enough statistical efficiency to outperform algorithms that simply process a random subset of the data. This volume offers researchers and engineers practical solutions for learning from large scale datasets, with detailed descriptions of algorithms and experiments carried out on realistically large datasets. At the same time it offers researchers information that can address the relative lack of theoretical grounding for many useful algorithms. After a detailed description of state-of-the-art support vector machine technology, an introduction of the essential concepts discussed in the volume, and a comparison of primal and dual optimization techniques, the book progresses from well-understood techniques to more novel and controversial approaches. Many contributors have made their code and data available online for further experimentation. Topics covered include fast implementations of known algorithms, approximations that are amenable to theoretical guarantees, and algorithms that perform well in practice but are difficult to analyze theoretically.

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Bottou, L., Chapelle, O., DeCoste, D., Weston, J. Large-Scale Kernel Machines pages: 416, Neural Information Processing Series, MIT Press, Cambridge, MA, USA, September 2007 (book)

Web [BibTex]

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Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference

Schölkopf, B., Platt, J., Hofmann, T.

Proceedings of the Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006), pages: 1690, MIT Press, Cambridge, MA, USA, 20th Annual Conference on Neural Information Processing Systems (NIPS), September 2007 (proceedings)

Abstract
The annual Neural Information Processing Systems (NIPS) conference is the flagship meeting on neural computation and machine learning. It draws a diverse group of attendees--physicists, neuroscientists, mathematicians, statisticians, and computer scientists--interested in theoretical and applied aspects of modeling, simulating, and building neural-like or intelligent systems. The presentations are interdisciplinary, with contributions in algorithms, learning theory, cognitive science, neuroscience, brain imaging, vision, speech and signal processing, reinforcement learning, and applications. Only twenty-five percent of the papers submitted are accepted for presentation at NIPS, so the quality is exceptionally high. This volume contains the papers presented at the December 2006 meeting, held in Vancouver.

Web [BibTex]

Schölkopf, B., Platt, J., Hofmann, T. Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference Proceedings of the Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006), pages: 1690, MIT Press, Cambridge, MA, USA, 20th Annual Conference on Neural Information Processing Systems (NIPS), September 2007 (proceedings)

Web [BibTex]

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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.

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

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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.

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

PDF [BibTex]

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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.

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

PDF [BibTex]

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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.

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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)

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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.

PDF Web [BibTex]

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

PDF Web [BibTex]

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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.

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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)

PDF [BibTex]

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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.

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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)

PDF [BibTex]

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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.

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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)

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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.

PDF link (url) [BibTex]

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]

2002

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Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

Schölkopf, B., Smola, A.

pages: 644, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, December 2002, Parts of this book, including an introduction to kernel methods, can be downloaded here. (book)

Abstract
In the 1990s, a new type of learning algorithm was developed, based on results from statistical learning theory: the Support Vector Machine (SVM). This gave rise to a new class of theoretically elegant learning machines that use a central concept of SVMs-kernels—for a number of learning tasks. Kernel machines provide a modular framework that can be adapted to different tasks and domains by the choice of the kernel function and the base algorithm. They are replacing neural networks in a variety of fields, including engineering, information retrieval, and bioinformatics. Learning with Kernels provides an introduction to SVMs and related kernel methods. Although the book begins with the basics, it also includes the latest research. It provides all of the concepts necessary to enable a reader equipped with some basic mathematical knowledge to enter the world of machine learning using theoretically well-founded yet easy-to-use kernel algorithms and to understand and apply the powerful algorithms that have been developed over the last few years.

Web [BibTex]

2002

Schölkopf, B., Smola, A. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond pages: 644, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, December 2002, Parts of this book, including an introduction to kernel methods, can be downloaded here. (book)

Web [BibTex]

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Kernel Dependency Estimation

Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V.

(98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)

Abstract
We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. Output kernels also make it possible to encode prior information and/or invariances in the loss function in an elegant way. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images.

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Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V. Kernel Dependency Estimation (98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)

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Global Geometry of SVM Classifiers

Zhou, D., Xiao, B., Zhou, H., Dai, R.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)

Abstract
We construct an geometry framework for any norm Support Vector Machine (SVM) classifiers. Within this framework, separating hyperplanes, dual descriptions and solutions of SVM classifiers are constructed by a purely geometric fashion. In contrast with the optimization theory used in SVM classifiers, we have no complicated computations any more. Each step in our theory is guided by elegant geometric intuitions.

PDF PostScript [BibTex]

Zhou, D., Xiao, B., Zhou, H., Dai, R. Global Geometry of SVM Classifiers Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)

PDF PostScript [BibTex]

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Computationally Efficient Face Detection

Romdhani, S., Torr, P., Schölkopf, B., Blake, A.

(MSR-TR-2002-69), Microsoft Research, June 2002 (techreport)

Web [BibTex]

Romdhani, S., Torr, P., Schölkopf, B., Blake, A. Computationally Efficient Face Detection (MSR-TR-2002-69), Microsoft Research, June 2002 (techreport)

Web [BibTex]

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Kernel-based nonlinear blind source separation

Harmeling, S., Ziehe, A., Kawanabe, M., Müller, K.

EU-Project BLISS, January 2002 (techreport)

GZIP [BibTex]

Harmeling, S., Ziehe, A., Kawanabe, M., Müller, K. Kernel-based nonlinear blind source separation EU-Project BLISS, January 2002 (techreport)

GZIP [BibTex]

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A compression approach to support vector model selection

von Luxburg, U., Bousquet, O., Schölkopf, B.

(101), Max Planck Institute for Biological Cybernetics, 2002, see more detailed JMLR version (techreport)

Abstract
In this paper we investigate connections between statistical learning theory and data compression on the basis of support vector machine (SVM) model selection. Inspired by several generalization bounds we construct ``compression coefficients'' for SVMs, which measure the amount by which the training labels can be compressed by some classification hypothesis. The main idea is to relate the coding precision of this hypothesis to the width of the margin of the SVM. The compression coefficients connect well known quantities such as the radius-margin ratio R^2/rho^2, the eigenvalues of the kernel matrix and the number of support vectors. To test whether they are useful in practice we ran model selection experiments on several real world datasets. As a result we found that compression coefficients can fairly accurately predict the parameters for which the test error is minimized.

[BibTex]

von Luxburg, U., Bousquet, O., Schölkopf, B. A compression approach to support vector model selection (101), Max Planck Institute for Biological Cybernetics, 2002, see more detailed JMLR version (techreport)

[BibTex]

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Feature Selection and Transduction for Prediction of Molecular Bioactivity for Drug Design

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

Max Planck Institute for Biological Cybernetics / Biowulf Technologies, 2002 (techreport)

Web [BibTex]

Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B. Feature Selection and Transduction for Prediction of Molecular Bioactivity for Drug Design Max Planck Institute for Biological Cybernetics / Biowulf Technologies, 2002 (techreport)

Web [BibTex]

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Observations on the Nyström Method for Gaussian Process Prediction

Williams, C., Rasmussen, C., Schwaighofer, A., Tresp, V.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2002 (techreport)

Abstract
A number of methods for speeding up Gaussian Process (GP) prediction have been proposed, including the Nystr{\"o}m method of Williams and Seeger (2001). In this paper we focus on two issues (1) the relationship of the Nystr{\"o}m method to the Subset of Regressors method (Poggio and Girosi 1990; Luo and Wahba, 1997) and (2) understanding in what circumstances the Nystr{\"o}m approximation would be expected to provide a good approximation to exact GP regression.

PostScript [BibTex]

Williams, C., Rasmussen, C., Schwaighofer, A., Tresp, V. Observations on the Nyström Method for Gaussian Process Prediction Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2002 (techreport)

PostScript [BibTex]

1997

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Homing by parameterized scene matching

Franz, M., Schölkopf, B., Bülthoff, H.

(46), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, Febuary 1997 (techreport)

Abstract
In visual homing tasks, animals as well as robots can compute their movements from the current view and a snapshot taken at a home position. Solving this problem exactly would require knowledge about the distances to visible landmarks, information, which is not directly available to passive vision systems. We propose a homing scheme that dispenses with accurate distance information by using parameterized disparity fields. These are obtained from an approximation that incorporates prior knowledge about perspective distortions of the visual environment. A mathematical analysis proves that the approximation does not prevent the scheme from approaching the goal with arbitrary accuracy. Mobile robot experiments are used to demonstrate the practical feasibility of the approach.

[BibTex]

1997

Franz, M., Schölkopf, B., Bülthoff, H. Homing by parameterized scene matching (46), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, Febuary 1997 (techreport)

[BibTex]

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Support vector learning

Schölkopf, B.

pages: 173, Oldenbourg, München, Germany, 1997, Zugl.: Berlin, Techn. Univ., Diss., 1997 (book)

PDF GZIP [BibTex]

Schölkopf, B. Support vector learning pages: 173, Oldenbourg, München, Germany, 1997, Zugl.: Berlin, Techn. Univ., Diss., 1997 (book)

PDF GZIP [BibTex]

1995

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A New Method for Constructing Artificial Neural Networks

Vapnik, V., Burges, C., Schölkopf, B.

AT & T Bell Laboratories, 1995 (techreport)

[BibTex]

1995

Vapnik, V., Burges, C., Schölkopf, B. A New Method for Constructing Artificial Neural Networks AT & T Bell Laboratories, 1995 (techreport)

[BibTex]