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2006


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Estimating Predictive Variances with Kernel Ridge Regression

Cawley, G., Talbot, N., Chapelle, O.

In MLCW 2005, pages: 56-77, (Editors: Quinonero-Candela, J. , I. Dagan, B. Magnini, F. D‘Alché-Buc), Springer, Berlin, Germany, First PASCAL Machine Learning Challenges Workshop, April 2006 (inproceedings)

Abstract
In many regression tasks, in addition to an accurate estimate of the conditional mean of the target distribution, an indication of the predictive uncertainty is also required. There are two principal sources of this uncertainty: the noise process contaminating the data and the uncertainty in estimating the model parameters based on a limited sample of training data. Both of them can be summarised in the predictive variance which can then be used to give confidence intervals. In this paper, we present various schemes for providing predictive variances for kernel ridge regression, especially in the case of a heteroscedastic regression, where the variance of the noise process contaminating the data is a smooth function of the explanatory variables. The use of leave-one-out cross-validation is shown to eliminate the bias inherent in estimates of the predictive variance. Results obtained on all three regression tasks comprising the predictive uncertainty challenge demonstrate the value of this approach.

PDF Web DOI [BibTex]

2006

PDF Web DOI [BibTex]


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Machine Learning Methods For Estimating Operator Equations

Steinke, F., Schölkopf, B.

In Proceedings of the 14th IFAC Symposium on System Identification (SYSID 2006), pages: 6, (Editors: B Ninness and H Hjalmarsson), Elsevier, Oxford, United Kingdom, 14th IFAC Symposium on System Identification (SYSID), March 2006 (inproceedings)

Abstract
We consider the problem of fitting a linear operator induced equation to point sampled data. In order to do so we systematically exploit the duality between minimizing a regularization functional derived from an operator and kernel regression methods. Standard machine learning model selection algorithms can then be interpreted as a search of the equation best fitting given data points. For many kernels this operator induced equation is a linear differential equation. Thus, we link a continuous-time system identification task with common machine learning methods. The presented link opens up a wide variety of methods to be applied to this system identification problem. In a series of experiments we demonstrate an example algorithm working on non-uniformly spaced data, giving special focus to the problem of identifying one system from multiple data recordings.

PDF Web [BibTex]

PDF Web [BibTex]


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Implicit Volterra and Wiener Series for Higher-Order Image Analysis

Franz, M., Schölkopf, B.

In Advances in Data Analysis: Proceedings of the 30th Annual Conference of The Gesellschaft für Klassifikation, 30, pages: 1, March 2006 (inproceedings)

Abstract
The computation of classical higher-order statistics such as higher-order moments or spectra is difficult for images due to the huge number of terms to be estimated and interpreted. We propose an alternative approach in which multiplicative pixel interactions are described by a series of Wiener functionals. Since the functionals are estimated implicitly via polynomial kernels, the combinatorial explosion associated with the classical higher-order statistics is avoided. In addition, the kernel framework allows for estimating infinite series expansions and for the regularized estimation of the Wiener series. First results show that image structures such as lines or corners can be predicted correctly, and that pixel interactions up to the order of five play an important role in natural images.

PDF [BibTex]

PDF [BibTex]


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Gaussian Processes for Machine Learning

Rasmussen, CE., Williams, CKI.

pages: 248, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, January 2006 (book)

Abstract
Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Web [BibTex]

Web [BibTex]


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Causal Inference by Choosing Graphs with Most Plausible Markov Kernels

Sun, X., Janzing, D., Schölkopf, B.

In Proceedings of the 9th International Symposium on Artificial Intelligence and Mathematics, pages: 1-11, ISAIM, January 2006 (inproceedings)

Abstract
We propose a new inference rule for estimating causal structure that underlies the observed statistical dependencies among n random variables. Our method is based on comparing the conditional distributions of variables given their direct causes (the so-called Markov kernels") for all hypothetical causal directions and choosing the most plausible one. We consider those Markov kernels most plausible, which maximize the (conditional) entropies constrained by their observed first moment (expectation) and second moments (variance and covariance with its direct causes) based on their given domain. In this paper, we discuss our inference rule for causal relationships between two variables in detail, apply it to a real-world temperature data set with known causality and show that our method provides a correct result for the example.

PDF Web [BibTex]

PDF Web [BibTex]


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Learning operational space control

Peters, J., Schaal, S.

In Robotics: Science and Systems II (RSS 2006), pages: 255-262, (Editors: Gaurav S. Sukhatme and Stefan Schaal and Wolfram Burgard and Dieter Fox), Cambridge, MA: MIT Press, RSS , 2006, clmc (inproceedings)

Abstract
While operational space control is of essential importance for robotics and well-understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in face of modeling errors, which are inevitable in complex robots, e.g., humanoid robots. In such cases, learning control methods can offer an interesting alternative to analytical control algorithms. However, the resulting learning problem is ill-defined as it requires to learn an inverse mapping of a usually redundant system, which is well known to suffer from the property of non-covexity of the solution space, i.e., the learning system could generate motor commands that try to steer the robot into physically impossible configurations. A first important insight for this paper is that, nevertheless, a physically correct solution to the inverse problem does exits when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on a recent insight that many operational space controllers can be understood in terms of a constraint optimal control problem. The cost function associated with this optimal control problem allows us to formulate a learning algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the view of machine learning, the learning problem corresponds to a reinforcement learning problem that maximizes an immediate reward and that employs an expectation-maximization policy search algorithm. Evaluations on a three degrees of freedom robot arm illustrate the feasability of our suggested approach.

link (url) [BibTex]

link (url) [BibTex]


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Reinforcement Learning for Parameterized Motor Primitives

Peters, J., Schaal, S.

In Proceedings of the 2006 International Joint Conference on Neural Networks, pages: 73-80, IJCNN, 2006, clmc (inproceedings)

Abstract
One of the major challenges in both action generation for robotics and in the understanding of human motor control is to learn the "building blocks of movement generation", called motor primitives. Motor primitives, as used in this paper, are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. While a lot of progress has been made in teaching parameterized motor primitives using supervised or imitation learning, the self-improvement by interaction of the system with the environment remains a challenging problem. In this paper, we evaluate different reinforcement learning approaches for improving the performance of parameterized motor primitives. For pursuing this goal, we highlight the difficulties with current reinforcement learning methods, and outline both established and novel algorithms for the gradient-based improvement of parameterized policies. We compare these algorithms in the context of motor primitive learning, and show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm.

link (url) DOI [BibTex]

link (url) DOI [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

Web [BibTex]


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Gender Classification of Human Faces

Graf, A., Wichmann, F.

In Biologically Motivated Computer Vision, pages: 1-18, (Editors: Bülthoff, H. H., S.W. Lee, T. A. Poggio and C. Wallraven), Springer, Berlin, Germany, Second International Workshop on Biologically Motivated Computer Vision (BMCV), November 2002 (inproceedings)

Abstract
This paper addresses the issue of combining pre-processing methods—dimensionality reduction using Principal Component Analysis (PCA) and Locally Linear Embedding (LLE)—with Support Vector Machine (SVM) classification for a behaviorally important task in humans: gender classification. A processed version of the MPI head database is used as stimulus set. First, summary statistics of the head database are studied. Subsequently the optimal parameters for LLE and the SVM are sought heuristically. These values are then used to compare the original face database with its processed counterpart and to assess the behavior of a SVM with respect to changes in illumination and perspective of the face images. Overall, PCA was superior in classification performance and allowed linear separability.

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


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Insect-Inspired Estimation of Self-Motion

Franz, MO., Chahl, JS.

In Biologically Motivated Computer Vision, (2525):171-180, LNCS, (Editors: Bülthoff, H.H. , S.W. Lee, T.A. Poggio, C. Wallraven), Springer, Berlin, Germany, Second International Workshop on Biologically Motivated Computer Vision (BMCV), November 2002 (inproceedings)

Abstract
The tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion. In this study, we examine whether a simplified linear model of these neurons can be used to estimate self-motion from the optic flow. We present a theory for the construction of an optimal linear estimator incorporating prior knowledge about the environment. The optimal estimator is tested on a gantry carrying an omnidirectional vision sensor. The experiments show that the proposed approach leads to accurate and robust estimates of rotation rates, whereas translation estimates turn out to be less reliable.

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


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Combining sensory Information to Improve Visualization

Ernst, M., Banks, M., Wichmann, F., Maloney, L., Bülthoff, H.

In Proceedings of the Conference on Visualization ‘02 (VIS ‘02), pages: 571-574, (Editors: Moorhead, R. , M. Joy), IEEE, Piscataway, NJ, USA, IEEE Conference on Visualization (VIS '02), October 2002 (inproceedings)

Abstract
Seemingly effortlessly the human brain reconstructs the three-dimensional environment surrounding us from the light pattern striking the eyes. This seems to be true across almost all viewing and lighting conditions. One important factor for this apparent easiness is the redundancy of information provided by the sensory organs. For example, perspective distortions, shading, motion parallax, or the disparity between the two eyes' images are all, at least partly, redundant signals which provide us with information about the three-dimensional layout of the visual scene. Our brain uses all these different sensory signals and combines the available information into a coherent percept. In displays visualizing data, however, the information is often highly reduced and abstracted, which may lead to an altered perception and therefore a misinterpretation of the visualized data. In this panel we will discuss mechanisms involved in the combination of sensory information and their implications for simulations using computer displays, as well as problems resulting from current display technology such as cathode-ray tubes.

PDF Web [BibTex]

PDF Web [BibTex]


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Incorporating Invariances in Non-Linear Support Vector Machines

Chapelle, O., Schölkopf, B.

In Advances in Neural Information Processing Systems 14, pages: 609-616, (Editors: TG Dietterich and S Becker and Z Ghahramani), MIT Press, Cambridge, MA, USA, 15th Annual Neural Information Processing Systems Conference (NIPS), September 2002 (inproceedings)

Abstract
The choice of an SVM kernel corresponds to the choice of a representation of the data in a feature space and, to improve performance, it should therefore incorporate prior knowledge such as known transformation invariances. We propose a technique which extends earlier work and aims at incorporating invariances in nonlinear kernels. We show on a digit recognition task that the proposed approach is superior to the Virtual Support Vector method, which previously had been the method of choice.

PDF Web [BibTex]

PDF Web [BibTex]


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A kernel approach for learning from almost orthogonal patterns

Schölkopf, B., Weston, J., Eskin, E., Leslie, C., Noble, W.

In Principles of Data Mining and Knowledge Discovery, Lecture Notes in Computer Science, 2430/2431, pages: 511-528, Lecture Notes in Computer Science, (Editors: T Elomaa and H Mannila and H Toivonen), Springer, Berlin, Germany, 13th European Conference on Machine Learning (ECML) and 6th European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD'2002), 2002 (inproceedings)

PostScript DOI [BibTex]

PostScript DOI [BibTex]


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Luminance Artifacts on CRT Displays

Wichmann, F.

In IEEE Visualization, pages: 571-574, (Editors: Moorhead, R.; Gross, M.; Joy, K. I.), IEEE Visualization, 2002 (inproceedings)

Abstract
Most visualization panels today are still built around cathode-ray tubes (CRTs), certainly on personal desktops at work and at home. Whilst capable of producing pleasing images for common applications ranging from email writing to TV and DVD presentation, it is as well to note that there are a number of nonlinear transformations between input (voltage) and output (luminance) which distort the digital and/or analogue images send to a CRT. Some of them are input-independent and hence easy to fix, e.g. gamma correction, but others, such as pixel interactions, depend on the content of the input stimulus and are thus harder to compensate for. CRT-induced image distortions cause problems not only in basic vision research but also for applications where image fidelity is critical, most notably in medicine (digitization of X-ray images for diagnostic purposes) and in forms of online commerce, such as the online sale of images, where the image must be reproduced on some output device which will not have the same transfer function as the customer's CRT. I will present measurements from a number of CRTs and illustrate how some of their shortcomings may be problematic for the aforementioned applications.

[BibTex]

[BibTex]