Header logo is


2008


no image
Information Consistency of Nonparametric Gaussian Process Methods

Seeger, MW., Kakade, SM., Foster, DP.

IEEE Transactions on Information Theory, 54(5):2376-2382, May 2008 (article)

Abstract
Abstract—Bayesian nonparametric models are widely and successfully used for statistical prediction. While posterior consistency properties are well studied in quite general settings, results have been proved using abstract concepts such as metric entropy, and they come with subtle conditions which are hard to validate and not intuitive when applied to concrete models. Furthermore, convergence rates are difficult to obtain. By focussing on the concept of information consistency for Bayesian Gaussian process (GP)models, consistency results and convergence rates are obtained via a regret bound on cumulative log loss. These results depend strongly on the covariance function of the prior process, thereby giving a novel interpretation to penalization with reproducing kernel Hilbert space norms and to commonly used covariance function classes and their parameters. The proof of the main result employs elementary convexity arguments only. A theorem of Widom is used in order to obtain precise convergence rates for several covariance functions widely used in practice.

ei

Web DOI [BibTex]

2008


Web DOI [BibTex]


no image
Causal inference from statistical data

Sun, X.

Biologische Kybernetik, Technische Hochschule Karlsruhe, Karlsruhe, Germany, April 2008 (phdthesis)

ei

Web [BibTex]

Web [BibTex]


no image
Pairwise Correlations and Multineuronal Firing Patterns in Primary Visual Cortex

Berens, P.

Biologische Kybernetik, Eberhard Karls Universität Tübingen, Tübingen, Germany, April 2008 (diplomathesis)

ei

[BibTex]

[BibTex]


no image
Relating the Thermodynamic Arrow of Time to the Causal Arrow

Allahverdyan, A., Janzing, D.

Journal of Statistical Mechanics, 2008(P04001):1-21, April 2008 (article)

Abstract
Consider a Hamiltonian system that consists of a slow subsystem S and a fast subsystem F. The autonomous dynamics of S is driven by an effective Hamiltonian, but its thermodynamics is unexpected. We show that a well-defined thermodynamic arrow of time (second law) emerges for S whenever there is a well-defined causal arrow from S to F and the back-action is negligible. This is because the back-action of F on S is described by a non-globally Hamiltonian Born–Oppenheimer term that violates the Liouville theorem, and makes the second law inapplicable to S. If S and F are mixing, under the causal arrow condition they are described by microcanonical distributions P(S) and P(S|F). Their structure supports a causal inference principle proposed recently in machine learning.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
Generalization and Similarity in Exemplar Models of Categorization: Insights from Machine Learning

Jäkel, F., Schölkopf, B., Wichmann, F.

Psychonomic Bulletin and Review, 15(2):256-271, April 2008 (article)

Abstract
Exemplar theories of categorization depend on similarity for explaining subjects’ ability to generalize to new stimuli. A major criticism of exemplar theories concerns their lack of abstraction mechanisms and thus, seemingly, generalization ability. Here, we use insights from machine learning to demonstrate that exemplar models can actually generalize very well. Kernel methods in machine learning are akin to exemplar models and very successful in real-world applications. Their generalization performance depends crucially on the chosen similaritymeasure. While similarity plays an important role in describing generalization behavior it is not the only factor that controls generalization performance. In machine learning, kernel methods are often combined with regularization techniques to ensure good generalization. These same techniques are easily incorporated in exemplar models. We show that the Generalized Context Model (Nosofsky, 1986) and ALCOVE (Kruschke, 1992) are closely related to a statistical model called kernel logistic regression. We argue that generalization is central to the enterprise of understanding categorization behavior and suggest how insights from machine learning can offer some guidance. Keywords: kernel, similarity, regularization, generalization, categorization.

ei

PDF Web DOI [BibTex]


no image
Manifold-valued Thin-plate Splines with Applications in Computer Graphics

Steinke, F., Hein, M., Peters, J., Schölkopf, B.

Computer Graphics Forum, 27(2):437-448, April 2008 (article)

Abstract
We present a generalization of thin-plate splines for interpolation and approximation of manifold-valued data, and demonstrate its usefulness in computer graphics with several applications from different fields. The cornerstone of our theoretical framework is an energy functional for mappings between two Riemannian manifolds which is independent of parametrization and respects the geometry of both manifolds. If the manifolds are Euclidean, the energy functional reduces to the classical thin-plate spline energy. We show how the resulting optimization problems can be solved efficiently in many cases. Our example applications range from orientation interpolation and motion planning in animation over geometric modelling tasks to color interpolation.

ei

PDF AVI Web DOI [BibTex]


no image
The Metric Nearness Problem

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

SIAM Journal on Matrix Analysis and Applications, 30(1):375-396, April 2008 (article)

Abstract
Metric nearness refers to the problem of optimally restoring metric properties to distance measurements that happen to be nonmetric due to measurement errors or otherwise. Metric data can be important in various settings, for example, in clustering, classification, metric-based indexing, query processing, and graph theoretic approximation algorithms. This paper formulates and solves the metric nearness problem: Given a set of pairwise dissimilarities, find a “nearest” set of distances that satisfy the properties of a metric—principally the triangle inequality. For solving this problem, the paper develops efficient triangle fixing algorithms that are based on an iterative projection method. An intriguing aspect of the metric nearness problem is that a special case turns out to be equivalent to the all pairs shortest paths problem. The paper exploits this equivalence and develops a new algorithm for the latter problem using a primal-dual method. Applications to graph clustering are provided as an illustratio n. We include experiments that demonstrate the computational superiority of triangle fixing over general purpose convex programming software. Finally, we conclude by suggesting various useful extensions and generalizations to metric nearness.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
Bayesian Inference and Optimal Design for the Sparse Linear Model

Seeger, MW.

Journal of Machine Learning Research, 9, pages: 759-813, April 2008 (article)

Abstract
The linear model with sparsity-favouring prior on the coefficients has important applications in many different domains. In machine learning, most methods to date search for maximum a posteriori sparse solutions and neglect to represent posterior uncertainties. In this paper, we address problems of Bayesian optimal design (or experiment planning), for which accurate estimates of uncertainty are essential. To this end, we employ expectation propagation approximate inference for the linear model with Laplace prior, giving new insight into numerical stability properties and proposing a robust algorithm. We also show how to estimate model hyperparameters by empirical Bayesian maximisation of the marginal likelihood, and propose ideas in order to scale up the method to very large underdetermined problems. We demonstrate the versatility of our framework on the application of gene regulatory network identification from micro-array expression data, where both the Laplace prior and the active experimental design approach are shown to result in significant improvements. We also address the problem of sparse coding of natural images, and show how our framework can be used for compressive sensing tasks.

ei

PDF PDF [BibTex]

PDF PDF [BibTex]


no image
Consistency of Spectral Clustering

von Luxburg, U., Belkin, M., Bousquet, O.

Annals of Statistics, 36(2):555-586, April 2008 (article)

Abstract
Consistency is a key property of statistical algorithms when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of the popular family of spectral clustering algorithms, which clusters the data with the help of eigenvectors of graph Laplacian matrices. We develop new methods to establish that for increasing sample size, those eigenvectors converge to the eigenvectors of certain limit operators. As a result we can prove that one of the two major classes of spectral clustering (normalized clustering) converges under very general conditions, while the other (unnormalized clustering) is only consistent under strong additional assumptions, which are not always satisfied in real data. We conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


no image
Plant Classification from Bat-Like Echolocation Signals

Yovel, Y., Franz, MO., Stilz, P., Schnitzler, H-U.

PLoS Computational Biology, 4(3, e1000032):1-13, March 2008 (article)

Abstract
Classification of plants according to their echoes is an elementary component of bat behavior that plays an important role in spatial orientation and food acquisition. Vegetation echoes are, however, highly complex stochastic signals: from an acoustical point of view, a plant can be thought of as a three-dimensional array of leaves reflecting the emitted bat call. The received echo is therefore a superposition of many reflections. In this work we suggest that the classification of these echoes might not be such a troublesome routine for bats as formerly thought. We present a rather simple approach to classifying signals from a large database of plant echoes that were created by ensonifying plants with a frequency-modulated bat-like ultrasonic pulse. Our algorithm uses the spectrogram of a single echo from which it only uses features that are undoubtedly accessible to bats. We used a standard machine learning algorithm (SVM) to automatically extract suitable linear combinations of time and frequency cues from the spectrograms such that classification with high accuracy is enabled. This demonstrates that ultrasonic echoes are highly informative about the species membership of an ensonified plant, and that this information can be extracted with rather simple, biologically plausible analysis. Thus, our findings provide a new explanatory basis for the poorly understood observed abilities of bats in classifying vegetation and other complex objects.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
The role of stimulus correlations for population decoding in the retina

Schwartz, G., Macke, J., Berry, M.

Computational and Systems Neuroscience 2008 (COSYNE 2008), 5, pages: 172, March 2008 (poster)

ei

PDF Web [BibTex]

PDF Web [BibTex]


no image
Causal Reasoning by Evaluating the Complexity of Conditional Densities with Kernel Methods

Sun, X., Janzing, D., Schölkopf, B.

Neurocomputing, 71(7-9):1248-1256, March 2008 (article)

Abstract
We propose a method to quantify the complexity of conditional probability measures by a Hilbert space seminorm of the logarithm of its density. The concept of reproducing kernel Hilbert spaces (RKHSs) is a flexible tool to define such a seminorm by choosing an appropriate kernel. We present several examples with artificial data sets where our kernel-based complexity measure is consistent with our intuitive understanding of complexity of densities. The intention behind the complexity measure is to provide a new approach to inferring causal directions. The idea is that the factorization of the joint probability measure P(effect, cause) into P(effect|cause)P(cause) leads typically to "simpler" and "smoother" terms than the factorization into P(cause|effect)P(effect). Since the conventional constraint-based approach of causal discovery is not able to determine the causal direction between only two variables, our inference principle can in particular be useful when combined with other existing methods. We provide several simple examples with real-world data where the true causal directions indeed lead to simpler (conditional) densities.

ei

Web DOI [BibTex]


no image
Natural Actor-Critic

Peters, J., Schaal, S.

Neurocomputing, 71(7-9):1180-1190, March 2008 (article)

Abstract
In this paper, we suggest a novel reinforcement learning architecture, the Natural Actor-Critic. The actor updates are achieved using stochastic policy gradients em- ploying Amari’s natural gradient approach, while the critic obtains both the natural policy gradient and additional parameters of a value function simultaneously by lin- ear regression. We show that actor improvements with natural policy gradients are particularly appealing as these are independent of coordinate frame of the chosen policy representation, and can be estimated more efficiently than regular policy gra- dients. The critic makes use of a special basis function parameterization motivated by the policy-gradient compatible function approximation. We show that several well-known reinforcement learning methods such as the original Actor-Critic and Bradtke’s Linear Quadratic Q-Learning are in fact Natural Actor-Critic algorithms. Empirical evaluations illustrate the effectiveness of our techniques in comparison to previous methods, and also demonstrate their applicability for learning control on an anthropomorphic robot arm.

ei

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


no image
Inferring Spike Trains From Local Field Potentials

Rasch, M., Gretton, A., Murayama, Y., Maass, W., Logothetis, N.

Journal of Neurophysiology, 99(3):1461-1476, March 2008 (article)

Abstract
We investigated whether it is possible to infer spike trains solely on the basis of the underlying local field potentials (LFPs). Using support vector machines and linear regression models, we found that in the primary visual cortex (V1) of monkeys, spikes can indeed be inferred from LFPs, at least with moderate success. Although there is a considerable degree of variation across electrodes, the low-frequency structure in spike trains (in the 100-ms range) can be inferred with reasonable accuracy, whereas exact spike positions are not reliably predicted. Two kinds of features of the LFP are exploited for prediction: the frequency power of bands in the high gamma-range (40–90 Hz) and information contained in lowfrequency oscillations ( 10 Hz), where both phase and power modulations are informative. Information analysis revealed that both features code (mainly) independent aspects of the spike-to-LFP relationship, with the low-frequency LFP phase coding for temporally clustered spiking activity. Although both features and prediction quality are similar during seminatural movie stimuli and spontaneous activity, prediction performance during spontaneous activity degrades much more slowly with increasing electrode distance. The general trend of data obtained with anesthetized animals is qualitatively mirrored in that of a more limited data set recorded in V1 of non-anesthetized monkeys. In contrast to the cortical field potentials, thalamic LFPs (e.g., LFPs derived from recordings in the dorsal lateral geniculate nucleus) hold no useful information for predicting spiking activity.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
ISD: A Software Package for Bayesian NMR Structure Calculation

Rieping, W., Nilges, M., Habeck, M.

Bioinformatics, 24(8):1104-1105, February 2008 (article)

Abstract
SUMMARY: The conventional approach to calculating biomolecular structures from nuclear magnetic resonance (NMR) data is often viewed as subjective due to its dependence on rules of thumb for deriving geometric constraints and suitable values for theory parameters from noisy experimental data. As a result, it can be difficult to judge the precision of an NMR structure in an objective manner. The Inferential Structure Determination (ISD) framework, which has been introduced recently, addresses this problem by using Bayesian inference to derive a probability distribution that represents both the unknown structure and its uncertainty. It also determines additional unknowns, such as theory parameters, that normally need be chosen empirically. Here we give an overview of the ISD software package, which implements this methodology. AVAILABILITY: The program is available at http://www.bioc.cam.ac.uk/isd

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
Probabilistic Structure Calculation

Nilges, M., Habeck, M., Rieping, W.

Comptes Rendus Chimie, 11(4-5):356-369, February 2008 (article)

Abstract
Molecular structures are usually calculated from experimental data with some method of energy minimisation or non-linear optimisation. Key aims of a structure calculation are to estimate the coordinate uncertainty, and to provide a meaningful measure of the quality of the fit to the data. We discuss approaches to optimally combine prior information and experimental data and the connection to probability theory. We analyse the appropriate statistics for NOEs and NOE-derived distances, and the related question of restraint potentials. Finally, we will discuss approaches to determine the appropriate weight on the experimental evidence and to obtain in this way an estimate of the data quality from the structure calculation. Whereas objective estimates of coordinates and their uncertainties can only be obtained by a full Bayesian treatment of the problem, standard structure calculation methods continue to play an important role. To obtain the full benefit of these methods, they should be founded on a rigorous Baye sian analysis.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
Fast Projection-based Methods for the Least Squares Nonnegative Matrix Approximation Problem

Kim, D., Sra, S., Dhillon, I.

Statistical Analysis and Data Mining, 1(1):38-51, February 2008 (article)

Abstract
Nonnegative matrix approximation (NNMA) is a popular matrix decomposition technique that has proven to be useful across a diverse variety of fields with applications ranging from document analysis and image processing to bioinformatics and signal processing. Over the years, several algorithms for NNMA have been proposed, e.g. Lee and Seung‘s multiplicative updates, alternating least squares (ALS), and gradient descent-based procedures. However, most of these procedures suffer from either slow convergence, numerical instability, or at worst, serious theoretical drawbacks. In this paper, we develop a new and improved algorithmic framework for the least-squares NNMA problem, which is not only theoretically well-founded, but also overcomes many deficiencies of other methods. Our framework readily admits powerful optimization techniques and as concrete realizations we present implementations based on the Newton, BFGS and conjugate gradient methods. Our algorithms provide numerical resu lts supe rior to both Lee and Seung‘s method as well as to the alternating least squares heuristic, which was reported to work well in some situations but has no theoretical guarantees[1]. Our approach extends naturally to include regularization and box-constraints without sacrificing convergence guarantees. We present experimental results on both synthetic and real-world datasets that demonstrate the superiority of our methods, both in terms of better approximations as well as computational efficiency.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
A Unifying Probabilistic Framework for Analyzing Residual Dipolar Couplings

Habeck, M., Nilges, M., Rieping, W.

Journal of Biomolecular NMR, 40(2):135-144, February 2008 (article)

Abstract
Residual dipolar couplings provide complementary information to the nuclear Overhauser effect measurements that are traditionally used in biomolecular structure determination by NMR. In a de novo structure determination, however, lack of knowledge about the degree and orientation of molecular alignment complicates the analysis of dipolar coupling data. We present a probabilistic framework for analyzing residual dipolar couplings and demonstrate that it is possible to estimate the atomic coordinates, the complete molecular alignment tensor, and the error of the couplings simultaneously. As a by-product, we also obtain estimates of the uncertainty in the coordinates and the alignment tensor. We show that our approach encompasses existing methods for determining the alignment tensor as special cases, including least squares estimation, histogram fitting, and elimination of an explicit alignment tensor in the restraint energy.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


no image
Development and Application of a Python Scripting Framework for BCI2000

Schreiner, T.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, January 2008 (diplomathesis)

ei

[BibTex]

[BibTex]


no image
Efficient and Invariant Regularisation with Application to Computer Graphics

Walder, CJ.

Biologische Kybernetik, University of Queensland, Brisbane, Australia, January 2008 (phdthesis)

Abstract
This thesis develops the theory and practise of reproducing kernel methods. Many functional inverse problems which arise in, for example, machine learning and computer graphics, have been treated with practical success using methods based on a reproducing kernel Hilbert space perspective. This perspective is often theoretically convenient, in that many functional analysis problems reduce to linear algebra problems in these spaces. Somewhat more complex is the case of conditionally positive definite kernels, and we provide an introduction to both cases, deriving in a particularly elementary manner some key results for the conditionally positive definite case. A common complaint of the practitioner is the long running time of these kernel based algorithms. We provide novel ways of alleviating these problems by essentially using a non-standard function basis which yields computational advantages. That said, by doing so we must also forego the aforementioned theoretical conveniences, and hence need some additional analysis which we provide in order to make the approach practicable. We demonstrate that the method leads to state of the art performance on the problem of surface reconstruction from points. We also provide some analysis of kernels invariant to transformations such as translation and dilation, and show that this indicates the value of learning algorithms which use conditionally positive definite kernels. Correspondingly, we provide a few approaches for making such algorithms practicable. We do this either by modifying the kernel, or directly solving problems with conditionally positive definite kernels, which had previously only been solved with positive definite kernels. We demonstrate the advantage of this approach, in particular by attaining state of the art classification performance with only one free parameter.

ei

PDF [BibTex]

PDF [BibTex]


no image
Contour-propagation Algorithms for Semi-automated Reconstruction of Neural Processes

Macke, J., Maack, N., Gupta, R., Denk, W., Schölkopf, B., Borst, A.

Journal of Neuroscience Methods, 167(2):349-357, January 2008 (article)

Abstract
A new technique, ”Serial Block Face Scanning Electron Microscopy” (SBFSEM), allows for automatic sectioning and imaging of biological tissue with a scanning electron microscope. Image stacks generated with this technology have a resolution sufficient to distinguish different cellular compartments, including synaptic structures, which should make it possible to obtain detailed anatomical knowledge of complete neuronal circuits. Such an image stack contains several thousands of images and is recorded with a minimal voxel size of 10-20nm in the x and y- and 30nm in z-direction. Consequently, a tissue block of 1mm3 (the approximate volume of the Calliphora vicina brain) will produce several hundred terabytes of data. Therefore, highly automated 3D reconstruction algorithms are needed. As a first step in this direction we have developed semiautomated segmentation algorithms for a precise contour tracing of cell membranes. These algorithms were embedded into an easy-to-operate user interface, which allows direct 3D observation of the extracted objects during the segmentation of image stacks. Compared to purely manual tracing, processing time is greatly accelerated.

ei

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


no image
A Quantum-Statistical-Mechanical Extension of Gaussian Mixture Model

Tanaka, K., Tsuda, K.

Journal of Physics: Conference Series, 95(012023):1-9, January 2008 (article)

Abstract
We propose an extension of Gaussian mixture models in the statistical-mechanical point of view. The conventional Gaussian mixture models are formulated to divide all points in given data to some kinds of classes. We introduce some quantum states constructed by superposing conventional classes in linear combinations. Our extension can provide a new algorithm in classifications of data by means of linear response formulas in the statistical mechanics.

ei

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


no image
Learning to control in operational space

Peters, J., Schaal, S.

International Journal of Robotics Research, 27, pages: 197-212, 2008, clmc (article)

Abstract
One of the most general frameworks for phrasing control problems for complex, redundant robots is operational space control. However, while this framework 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 com- plex robots, e.g., humanoid robots. In this paper, we suggest a learning approach for opertional space control as a direct inverse model learning problem. A first important insight for this paper is that a physically cor- rect solution to the inverse problem with redundant degrees-of-freedom does exist when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on the insight that many operational space controllers can be understood in terms of a constrained optimal control problem. The cost function as- sociated with this optimal control problem allows us to formulate a learn- ing algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the machine learning point of view, this learning problem corre- sponds to a reinforcement learning problem that maximizes an immediate reward. We employ an expectation-maximization policy search algorithm in order to solve this problem. Evaluations on a three degrees of freedom robot arm are used to illustrate the suggested approach. The applica- tion to a physically realistic simulator of the anthropomorphic SARCOS Master arm demonstrates feasibility for complex high degree-of-freedom robots. We also show that the proposed method works in the setting of learning resolved motion rate control on real, physical Mitsubishi PA-10 medical robotics arm.

am ei

link (url) DOI [BibTex]

link (url) DOI [BibTex]


no image
Adaptation to a sub-optimal desired trajectory

M. Mistry, E. A. G. L. T. Y. S. S. M. K.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

am

PDF [BibTex]

PDF [BibTex]


no image
Operational space control: A theoretical and emprical comparison

Nakanishi, J., Cory, R., Mistry, M., Peters, J., Schaal, S.

International Journal of Robotics Research, 27(6):737-757, 2008, clmc (article)

Abstract
Dexterous manipulation with a highly redundant movement system is one of the hallmarks of hu- man motor skills. From numerous behavioral studies, there is strong evidence that humans employ compliant task space control, i.e., they focus control only on task variables while keeping redundant degrees-of-freedom as compliant as possible. This strategy is robust towards unknown disturbances and simultaneously safe for the operator and the environment. The theory of operational space con- trol in robotics aims to achieve similar performance properties. However, despite various compelling theoretical lines of research, advanced operational space control is hardly found in actual robotics imple- mentations, in particular new kinds of robots like humanoids and service robots, which would strongly profit from compliant dexterous manipulation. To analyze the pros and cons of different approaches to operational space control, this paper focuses on a theoretical and empirical evaluation of different methods that have been suggested in the literature, but also some new variants of operational space controllers. We address formulations at the velocity, acceleration and force levels. First, we formulate all controllers in a common notational framework, including quaternion-based orientation control, and discuss some of their theoretical properties. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm with several benchmark tasks. As an aside, we also introduce a novel parameter estimation algorithm for rigid body dynamics, which ensures physical consistency, as this issue was crucial for our successful robot implementations. Our extensive empirical results demonstrate that one of the simplified acceleration-based approaches can be advantageous in terms of task performance, ease of parameter tuning, and general robustness and compliance in face of inevitable modeling errors.

am

link (url) [BibTex]

link (url) [BibTex]


no image
A library for locally weighted projection regression

Klanke, S., Vijayakumar, S., Schaal, S.

Journal of Machine Learning Research, 9, pages: 623-626, 2008, clmc (article)

Abstract
In this paper we introduce an improved implementation of locally weighted projection regression (LWPR), a supervised learning algorithm that is capable of handling high-dimensional input data. As the key features, our code supports multi-threading, is available for multiple platforms, and provides wrappers for several programming languages.

am

link (url) [BibTex]

link (url) [BibTex]


no image
Optimization strategies in human reinforcement learning

Hoffmann, H., Theodorou, E., Schaal, S.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

am

PDF [BibTex]

PDF [BibTex]

2002


no image
Surface-slant-from-texture discrimination: Effects of slant level and texture type

Rosas, P., Wichmann, F., Wagemans, J.

Journal of Vision, 2(7):300, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Abstract
The problem of surface-slant-from-texture was studied psychophysically by measuring the performances of five human subjects in a slant-discrimination task with a number of different types of textures: uniform lattices, randomly displaced lattices, polka dots, Voronoi tessellations, orthogonal sinusoidal plaid patterns, fractal or 1/f noise, “coherent” noise and a “diffusion-based” texture (leopard skin-like). The results show: (1) Improving performance with larger slants for all textures. (2) A “non-symmetrical” performance around a particular slant characterized by a psychometric function that is steeper in the direction of the more slanted orientation. (3) For sufficiently large slants (66 deg) there are no major differences in performance between any of the different textures. (4) For slants at 26, 37 and 53 degrees, however, there are marked differences between the different textures. (5) The observed differences in performance across textures for slants up to 53 degrees are systematic within subjects, and nearly so across them. This allows a rank-order of textures to be formed according to their “helpfulness” — that is, how easy the discrimination task is when a particular texture is mapped on the surface. Polka dots tended to allow the best slant discrimination performance, noise patterns the worst up to the large slant of 66 degrees at which performance was almost independent of the particular texture chosen. Finally, our large number of 2AFC trials (approximately 2800 trials per texture across subjects) and associated tight confidence intervals may enable us to find out about which statistical properties of the textures could be responsible for surface-slant-from-texture estimation, with the ultimate goal of being able to predict observer performance for any arbitrary texture.

ei

Web DOI [BibTex]

2002


Web DOI [BibTex]


no image
Modelling Contrast Transfer in Spatial Vision

Wichmann, F.

Journal of Vision, 2(10):7, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Abstract
Much of our information about spatial vision comes from detection experiments involving low-contrast stimuli. Contrast discrimination experiments provide one way to explore the visual system's response to stimuli of higher contrast, the results of which allow different models of contrast processing (e.g. energy versus gain-control models) to be critically assessed (Wichmann & Henning, 1999). Studies of detection and discrimination using pulse train stimuli in noise, on the other hand, make predictions about the number, position and properties of noise sources within the processing stream (Henning, Bird & Wichmann, 2002). Here I report modelling results combining data from both sinusoidal and pulse train experiments in and without noise to arrive at a more tightly constrained model of early spatial vision.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
Pulse train detection and discrimination in pink noise

Henning, G., Wichmann, F., Bird, C.

Journal of Vision, 2(7):229, Second Annual Meeting of the Vision Sciences Society (VSS), November 2002 (poster)

Abstract
Much of our information about spatial vision comes from detection experiments involving low-contrast stimuli. Contrast discrimination experiments provide one way to explore the visual system's response to stimuli of higher contrast. We explored both detection and contrast discrimination performance with sinusoidal and "pulse-train" (or line) gratings. Both types of grating had a fundamental spatial frequency of 2.09-c/deg but the pulse-train, ideally, contains, in addition to its fundamental component, all the harmonics of the fundamental. Although the 2.09-c/deg pulse-train produced on the display was measured and shown to contain at least 8 harmonics at equal contrast, it was no more detectable than its most detectable component; no benefit from having additional information at the harmonics was measurable. The addition of broadband "pink" noise, designed to equalize the detectability of the components of the pulse train, made it about a factor of four more detectable than any of its components. However, in contrast-discrimination experiments, with an in-phase pedestal or masking grating of the same form and phase as the signal and 15% contrast, the noise did not improve the discrimination performance of the pulse train relative to that of its sinusoidal components. In contrast, a 2.09-c/deg "super train," constructed to have 8 equally detectable harmonics, was a factor of five more detectable than any of its components. We discuss the implications of these observations for models of early vision in particular the implications for possible sources of internal noise.

ei

Web DOI [BibTex]

Web DOI [BibTex]


no image
Constructing Boosting algorithms from SVMs: an application to one-class classification.

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

IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(9):1184-1199, September 2002 (article)

Abstract
We show via an equivalence of mathematical programs that a support vector (SV) algorithm can be translated into an equivalent boosting-like algorithm and vice versa. We exemplify this translation procedure for a new algorithm—one-class leveraging—starting from the one-class support vector machine (1-SVM). This is a first step toward unsupervised learning in a boosting framework. Building on so-called barrier methods known from the theory of constrained optimization, it returns a function, written as a convex combination of base hypotheses, that characterizes whether a given test point is likely to have been generated from the distribution underlying the training data. Simulations on one-class classification problems demonstrate the usefulness of our approach.

ei

DOI [BibTex]

DOI [BibTex]


no image
Phase information in the recognition of natural images

Braun, D., Wichmann, F., Gegenfurtner, K.

Perception, 31(ECVP Abstract Supplement):133, 25th European Conference on Visual Perception, August 2002 (poster)

Abstract
Fourier phase plays an important role in determining global image structure. For example, when the phase spectrum of an image of a flower is swapped with that of a tank, we usually perceive a tank, even though the amplitude spectrum is still that of the flower. Similarly, when the phase spectrum of an image is randomly swapped across frequencies, that is its Fourier energy is randomly distributed over the image, the resulting image becomes impossible to recognise. Our goal was to evaluate the effect of phase manipulations in a quantitative manner. Subjects viewed two images of natural scenes, one of which contained an animal (the target) embedded in the background. The spectra of the images were manipulated by adding random phase noise at each frequency. The phase noise was the independent variable, uniformly distributed between 0° and ±180°. Subjects were remarkably resistant to phase noise. Even with ±120° noise, subjects were still 75% correct. The proportion of correct answers closely followed the correlation between original and noise-distorted images. Thus it appears as if it was not the global phase information per se that determines our percept of natural images, but rather the effect of phase on local image features.

ei

Web [BibTex]

Web [BibTex]


no image
Forward models in visuomotor control

Mehta, B., Schaal, S.

J Neurophysiol, 88(2):942-53, August 2002, clmc (article)

Abstract
In recent years, an increasing number of research projects investigated whether the central nervous system employs internal models in motor control. While inverse models in the control loop can be identified more readily in both motor behavior and the firing of single neurons, providing direct evidence for the existence of forward models is more complicated. In this paper, we will discuss such an identification of forward models in the context of the visuomotor control of an unstable dynamic system, the balancing of a pole on a finger. Pole balancing imposes stringent constraints on the biological controller, as it needs to cope with the large delays of visual information processing while keeping the pole at an unstable equilibrium. We hypothesize various model-based and non-model-based control schemes of how visuomotor control can be accomplished in this task, including Smith Predictors, predictors with Kalman filters, tapped-delay line control, and delay-uncompensated control. Behavioral experiments with human participants allow exclusion of most of the hypothesized control schemes. In the end, our data support the existence of a forward model in the sensory preprocessing loop of control. As an important part of our research, we will provide a discussion of when and how forward models can be identified and also the possible pitfalls in the search for forward models in control.

am

link (url) [BibTex]

link (url) [BibTex]


no image
The contributions of color to recognition memory for natural scenes

Wichmann, F., Sharpe, L., Gegenfurtner, K.

Journal of Experimental Psychology: Learning, Memory and Cognition, 28(3):509-520, May 2002 (article)

Abstract
The authors used a recognition memory paradigm to assess the influence of color information on visual memory for images of natural scenes. Subjects performed 5-10% better for colored than for black-and-white images independent of exposure duration. Experiment 2 indicated little influence of contrast once the images were suprathreshold, and Experiment 3 revealed that performance worsened when images were presented in color and tested in black and white, or vice versa, leading to the conclusion that the surface property color is part of the memory representation. Experiments 4 and 5 exclude the possibility that the superior recognition memory for colored images results solely from attentional factors or saliency. Finally, the recognition memory advantage disappears for falsely colored images of natural scenes: The improvement in recognition memory depends on the color congruence of presented images with learned knowledge about the color gamut found within natural scenes. The results can be accounted for within a multiple memory systems framework.

ei

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


no image
Detection and discrimination in pink noise

Wichmann, F., Henning, G.

5, pages: 100, 5. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2002 (poster)

Abstract
Much of our information about early spatial vision comes from detection experiments involving low-contrast stimuli, which are not, perhaps, particularly "natural" stimuli. Contrast discrimination experiments provide one way to explore the visual system's response to stimuli of higher contrast whilst keeping the number of unknown parameters comparatively small. We explored both detection and contrast discrimination performance with sinusoidal and "pulse-train" (or line) gratings. Both types of grating had a fundamental spatial frequency of 2.09-c/deg but the pulse-train, ideally, contains, in addition to its fundamental component, all the harmonics of the fundamental. Although the 2.09-c/deg pulse-train produced on our display was measured using a high-performance digital camera (Photometrics) and shown to contain at least 8 harmonics at equal contrast, it was no more detectable than its most detectable component; no benefit from having additional information at the harmonics was measurable. The addition of broadband 1-D "pink" noise made it about a factor of four more detectable than any of its components. However, in contrast-discrimination experiments, with an in-phase pedestal or masking grating of the same form and phase as the signal and 15% contrast, the noise did not improve the discrimination performance of the pulse train relative to that of its sinusoidal components. We discuss the implications of these observations for models of early vision in particular the implications for possible sources of internal noise.

ei

Web [BibTex]

Web [BibTex]


no image
Training invariant support vector machines

DeCoste, D., Schölkopf, B.

Machine Learning, 46(1-3):161-190, January 2002 (article)

Abstract
Practical experience has shown that in order to obtain the best possible performance, prior knowledge about invariances of a classification problem at hand ought to be incorporated into the training procedure. We describe and review all known methods for doing so in support vector machines, provide experimental results, and discuss their respective merits. One of the significant new results reported in this work is our recent achievement of the lowest reported test error on the well-known MNIST digit recognition benchmark task, with SVM training times that are also significantly faster than previous SVM methods.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


no image
Contrast discrimination with sinusoidal gratings of different spatial frequency

Bird, C., Henning, G., Wichmann, F.

Journal of the Optical Society of America A, 19(7), pages: 1267-1273, 2002 (article)

Abstract
The detectability of contrast increments was measured as a function of the contrast of a masking or “pedestal” grating at a number of different spatial frequencies ranging from 2 to 16 cycles per degree of visual angle. The pedestal grating always had the same orientation, spatial frequency and phase as the signal. The shape of the contrast increment threshold versus pedestal contrast (TvC) functions depend of the performance level used to define the “threshold,” but when both axes are normalized by the contrast corresponding to 75% correct detection at each frequency, the (TvC) functions at a given performance level are identical. Confidence intervals on the slope of the rising part of the TvC functions are so wide that it is not possible with our data to reject Weber’s Law.

ei

PDF [BibTex]

PDF [BibTex]


no image
Support Vector Machines and Kernel Methods: The New Generation of Learning Machines

Cristianini, N., Schölkopf, B.

AI Magazine, 23(3):31-41, 2002 (article)

ei

[BibTex]


no image
Application of Monte Carlo Methods to Psychometric Function Fitting

Wichmann, F.

Proceedings of the 33rd European Conference on Mathematical Psychology, pages: 44, 2002 (poster)

Abstract
The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. Here I describe methods to (1) fitting psychometric functions, (2) assessing goodness-of-fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them. First I describe a constrained maximum-likelihood method for parameter estimation. Using Monte-Carlo simulations I demonstrate that it is important to have a fitting method that takes stimulus-independent errors (or "lapses") into account. Second, a number of goodness-of-fit tests are introduced. Because psychophysical data sets are usually rather small I advocate the use of Monte Carlo resampling techniques that do not rely on asymptotic theory for goodness-of-fit assessment. Third, a parametric bootstrap is employed to estimate the variability of fitted parameters and derived quantities such as thresholds and slopes. I describe how the bootstrap bridging assumption, on which the validity of the procedure depends, can be tested without incurring too high a cost in computation time. Finally I describe how the methods can be extended to test hypotheses concerning the form and shape of several psychometric functions. Software describing the methods is available (http://www.bootstrap-software.com/psignifit/), as well as articles describing the methods in detail (Wichmann&Hill, Perception&Psychophysics, 2001a,b).

ei

[BibTex]

[BibTex]


no image
Contrast discrimination with pulse-trains in pink noise

Henning, G., Bird, C., Wichmann, F.

Journal of the Optical Society of America A, 19(7), pages: 1259-1266, 2002 (article)

Abstract
Detection performance was measured with sinusoidal and pulse-train gratings. Although the 2.09-c/deg pulse-train, or line gratings, contained at least 8 harmonics all at equal contrast, they were no more detectable than their most detectable component. The addition of broadband pink noise designed to equalize the detectability of the components of the pulse train made the pulse train about a factor of four more detectable than any of its components. However, in contrast-discrimination experiments, with a pedestal or masking grating of the same form and phase as the signal and 15% contrast, the noise did not affect the discrimination performance of the pulse train relative to that obtained with its sinusoidal components. We discuss the implications of these observations for models of early vision in particular the implications for possible sources of internal noise.

ei

PDF [BibTex]

PDF [BibTex]


no image
Optimal linear estimation of self-motion - a real-world test of a model of fly tangential neurons

Franz, MO.

SAB 02 Workshop, Robotics as theoretical biology, 7th meeting of the International Society for Simulation of Adaptive Behaviour (SAB), (Editors: Prescott, T.; Webb, B.), 2002 (poster)

Abstract
The tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion (see example in Fig.1). 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 both about the distance distribution of the environment, and about the noise and self-motion statistics of the sensor. The optimal estimator is tested on a gantry carrying an omnidirectional vision sensor that can be moved along three translational and one rotational degree of freedom. The experiments indicate that the proposed approach yields accurate results for rotation estimates, independently of the current translation and scene layout. Translation estimates, however, turned out to be sensitive to simultaneous rotation and to the particular distance distribution of the scene. The gantry experiments confirm that the receptive field organization of the tangential neurons allows them, as an ensemble, to extract self-motion from the optic flow.

ei

PDF [BibTex]

PDF [BibTex]


no image
Scalable techniques from nonparameteric statistics for real-time robot learning

Schaal, S., Atkeson, C. G., Vijayakumar, S.

Applied Intelligence, 17(1):49-60, 2002, clmc (article)

Abstract
Locally weighted learning (LWL) is a class of techniques from nonparametric statistics that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional belief that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested on up to 90 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing by a humanoid robot arm, and inverse-dynamics learning for a seven and a 30 degree-of-freedom robot. In all these examples, the application of our statistical neural networks techniques allowed either faster or more accurate acquisition of motor control than classical control engineering.

am

link (url) [BibTex]

link (url) [BibTex]

2000


no image
A brachiating robot controller

Nakanishi, J., Fukuda, T., Koditschek, D. E.

IEEE Transactions on Robotics and Automation, 16(2):109-123, 2000, clmc (article)

Abstract
We report on our empirical studies of a new controller for a two-link brachiating robot. Motivated by the pendulum-like motion of an apeâ??s brachiation, we encode this task as the output of a â??target dynamical system.â? Numerical simulations indicate that the resulting controller solves a number of brachiation problems that we term the â??ladder,â? â??swing-up,â? and â??ropeâ? problems. Preliminary analysis provides some explanation for this success. The proposed controller is implemented on a physical system in our laboratory. The robot achieves behaviors including â??swing locomotionâ? and â??swing upâ? and is capable of continuous locomotion over several rungs of a ladder. We discuss a number of formal questions whose answers will be required to gain a full understanding of the strengths and weaknesses of this approach.

am

link (url) [BibTex]

2000


link (url) [BibTex]


no image
Interaction of rhythmic and discrete pattern generators in single joint movements

Sternad, D., Dean, W. J., Schaal, S.

Human Movement Science, 19(4):627-665, 2000, clmc (article)

Abstract
The study investigates a single-joint movement task that combines a translatory and cyclic component with the objective to investigate the interaction of discrete and rhythmic movement elements. Participants performed an elbow movement in the horizontal plane, oscillating at a prescribed frequency around one target and shifting to a second target upon a trigger signal, without stopping the oscillation. Analyses focused on extracting the mutual influences of the rhythmic and the discrete component of the task. Major findings are: (1) The onset of the discrete movement was confined to a limited phase window in the rhythmic cycle. (2) Its duration was influenced by the period of oscillation. (3) The rhythmic oscillation was "perturbed" by the discrete movement as indicated by phase resetting. On the basis of these results we propose a model for the coordination of discrete and rhythmic actions (K. Matsuoka, Sustained oscillations generated by mutually inhibiting neurons with adaptations, Biological Cybernetics 52 (1985) 367-376; Mechanisms of frequency and pattern control in the neural rhythm generators, Biological Cybernetics 56 (1987) 345-353). For rhythmic movements an oscillatory pattern generator is developed following models of half-center oscillations (D. Bullock, S. Grossberg, The VITE model: a neural command circuit for generating arm and articulated trajectories, in: J.A.S. Kelso, A.J. Mandel, M. F. Shlesinger (Eds.), Dynamic Patterns in Complex Systems. World Scientific. Singapore. 1988. pp. 305-326). For discrete movements a point attractor dynamics is developed close to the VITE model For each joint degree of freedom both pattern generators co-exist but exert mutual inhibition onto each other. The suggested modeling framework provides a unified account for both discrete and rhythmic movements on the basis of neuronal circuitry. Simulation results demonstrated that the effects observed in human performance can be replicated using the two pattern generators with a mutually inhibiting coupling.

am

link (url) [BibTex]

link (url) [BibTex]


no image
Dynamics of a bouncing ball in human performance

Sternad, D., Duarte, M., Katsumata, H., Schaal, S.

Physical Review E, 63(011902):1-8, 2000, clmc (article)

Abstract
On the basis of a modified bouncing-ball model, we investigated whether human movements utilize principles of dynamic stability in their performance of a similar movement task. Stability analyses of the model provided predictions about conditions indicative of a dynamically stable period-one regime. In a series of experiments, human subjects bounced a ball rhythmically on a racket and displayed these conditions supporting that they attuned to and exploited the dynamic stability properties of the task.

am

link (url) [BibTex]

link (url) [BibTex]

1995


no image
Memory-based neural networks for robot learning

Atkeson, C. G., Schaal, S.

Neurocomputing, 9, pages: 1-27, 1995, clmc (article)

Abstract
This paper explores a memory-based approach to robot learning, using memory-based neural networks to learn models of the task to be performed. Steinbuch and Taylor presented neural network designs to explicitly store training data and do nearest neighbor lookup in the early 1960s. In this paper their nearest neighbor network is augmented with a local model network, which fits a local model to a set of nearest neighbors. This network design is equivalent to a statistical approach known as locally weighted regression, in which a local model is formed to answer each query, using a weighted regression in which nearby points (similar experiences) are weighted more than distant points (less relevant experiences). We illustrate this approach by describing how it has been used to enable a robot to learn a difficult juggling task. Keywords: memory-based, robot learning, locally weighted regression, nearest neighbor, local models.

am

link (url) [BibTex]

1995


link (url) [BibTex]