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2008


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Structure from Behavior in Autonomous Agents

Martius, G., Fiedler, K., Herrmann, J.

In Proc. IEEE Intl. Conf. Intelligent Robots and Systems (IROS 2008), pages: 858 - 862, 2008 (inproceedings)

al

DOI [BibTex]

2008


DOI [BibTex]


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GdFe-Multilagen zur Vergrö\sserung des magnetischen Vortexkerns

Sackmann, V.

Universität Stuttgart, Stuttgart, 2008 (mastersthesis)

mms

[BibTex]

[BibTex]


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Dissipative Magnetisierungsdynamik: Ein Zugang über die ab-initio Elektronentheorie

Steiauf, D.

Universität Stuttgart, Stuttgart, 2008 (phdthesis)

mms

[BibTex]

[BibTex]


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The hole is important! The quest for ferromagnetism in doped ZnO

Tietze, T., Gacic, M., Schütz, G., Jakob, G., Brück, S., Goering, E.

{BESSY Highlights 2007}, pages: 14-15, 2008 (article)

mms

[BibTex]

[BibTex]


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Limitations of a simple quantum mechanical model: Magnetic dichroism in a relativistic one-electron atom

Rodr\’\iguez, J. C., Kostoglou, C., Singer, R., Seib, J., Fähnle, M.

{Physica Status Solidi (B)}, 245(4):735-739, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Impact of irradiation-induced point defects on electronically and ionically induced magnetic relaxation mechanisms in titano-magnetites

Walz, F., Brabers, V. A. M., Kronmüller, H.

{Physica Status Solidi (A)}, 205(12):2934-2942, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Polarization selective magnetic vortex dynamics and core reversal in rotating magnetic fields

Curcic, M., van Waeyenberge, B., Vansteenkiste, A., Weigand, M., Sackmann, V., Stoll, H., Fähnle, M., Tyliszczak, T., Woltersdorf, G., Back, C. H., Schütz, G.

{Physical Review Letters}, 101, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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X-ray spectroscopic investigations of Zn0.94Co0.06O thin films

Mayer, G., Fonin, M., Voss, S., Rüdiger, U., Goering, E.

{IEEE Transactions on Magnetics}, 44(11):2700-2703, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Experimental realization of graded L10-FePt/Fe composite media with perpendicular magnetization

Goll, D., Breitling, A., Gu, L., van Aken, P. A., Sigle, W.

{Journal of Applied Physics}, 104, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Hard magnetic L10 FePt thin films and nanopatterns

Breitling, A., Goll, D.

{Journal of Magnetism and Magnetic Materials}, 320, pages: 1449-1456, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Ma\ssgeschneiderte Speichermaterialien

Hirscher, M.

In Von Brennstoffzellen bis Leuchtdioden (Energie und Chemie - Ein Bündnis für die Zukunft), pages: 31-33, Deutsche Bunsen-Gesellschaft für Physikalische Chemie e.V., Frankfurt am Main, 2008 (incollection)

mms

[BibTex]

[BibTex]


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Spin-reorientation transition in Co/Pt multilayers on nanospheres

Eimüller, T., Ulbrich, T. C., Amaladass, E., Guhr, I. L., Tyliszczak, T., Albrecht, M.

{Physical Review B}, 77, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Non-destructive compositional analysis of historic organ reed pipes

Manescu, A., Fiori, F., Giuliani, A., Kardjilov, N., Kasztovszky, Z., Rustichelli, F., Straumal, B.

{Journal of Physics: Condensed Matter}, 20, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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An advanced magnetic reflectometer

Brück, S., Bauknecht, S., Ludescher, B., Goering, E., Schütz, G.

{Review of Scientific Instruments}, 79, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Computational model for movement learning under uncertain cost

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

In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

Abstract
Stochastic optimal control is a framework for computing control commands that lead to an optimal behavior under a given cost. Despite the long history of optimal control in engineering, it has been only recently applied to describe human motion. So far, stochastic optimal control has been mainly used in tasks that are already learned, such as reaching to a target. For learning, however, there are only few cases where optimal control has been applied. The main assumptions of stochastic optimal control that restrict its application to tasks after learning are the a priori knowledge of (1) a quadratic cost function (2) a state space model that captures the kinematics and/or dynamics of musculoskeletal system and (3) a measurement equation that models the proprioceptive and/or exteroceptive feedback. Under these assumptions, a sequence of control gains is computed that is optimal with respect to the prespecified cost function. In our work, we relax the assumption of the a priori known cost function and provide a computational framework for modeling tasks that involve learning. Typically, a cost function consists of two parts: one part that models the task constraints, like squared distance to goal at movement endpoint, and one part that integrates over the squared control commands. In learning a task, the first part of this cost function will be adapted. We use an expectation-maximization scheme for learning: the expectation step optimizes the task constraints through gradient descent of a reward function and the maximizing step optimizes the control commands. Our computational model is tested and compared with data given from a behavioral experiment. In this experiment, subjects sit in front of a drawing tablet and look at a screen onto which the drawing-pen's position is projected. Beginning from a start point, their task is to move with the pen through a target point presented on screen. Visual feedback about the pen's position is given only before movement onset. At the end of a movement, subjects get visual feedback only about the cost of this trial. In the mapping of the pen's position onto the screen, we added a bias (unknown to subject) and Gaussian noise. Therefore the cost is a function of this bias. The subjects were asked to reach to the target and minimize this cost over trials. In this behavioral experiment, subjects could learn the bias and thus showed reinforcement learning. With our computational model, we could model the learning process over trials. Particularly, the dependence on parameters of the reward function (Gaussian width) and the modulation of movement variance over time were similar in experiment and model.

am

[BibTex]

[BibTex]


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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]


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A Bayesian approach to empirical local linearizations for robotics

Ting, J., D’Souza, A., Vijayakumar, S., Schaal, S.

In International Conference on Robotics and Automation (ICRA2008), Pasadena, CA, USA, May 19-23, 2008, 2008, clmc (inproceedings)

Abstract
Local linearizations are ubiquitous in the control of robotic systems. Analytical methods, if available, can be used to obtain the linearization, but in complex robotics systems where the the dynamics and kinematics are often not faithfully obtainable, empirical linearization may be preferable. In this case, it is important to only use data for the local linearization that lies within a ``reasonable'' linear regime of the system, which can be defined from the Hessian at the point of the linearization -- a quantity that is not available without an analytical model. We introduce a Bayesian approach to solve statistically what constitutes a ``reasonable'' local regime. We approach this problem in the context local linear regression. In contrast to previous locally linear methods, we avoid cross-validation or complex statistical hypothesis testing techniques to find the appropriate local regime. Instead, we treat the parameters of the local regime probabilistically and use approximate Bayesian inference for their estimation. This approach results in an analytical set of iterative update equations that are easily implemented on real robotics systems for real-time applications. As in other locally weighted regressions, our algorithm also lends itself to complete nonlinear function approximation for learning empirical internal models. We sketch the derivation of our Bayesian method and provide evaluations on synthetic data and actual robot data where the analytical linearization was known.

am

link (url) [BibTex]

link (url) [BibTex]


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Do humans plan continuous trajectories in kinematic coordinates?

Hoffmann, H., Schaal, S.

In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

Abstract
The planning and execution of human arm movements is still unresolved. An ongoing controversy is whether we plan a movement in kinematic coordinates and convert these coordinates with an inverse internal model into motor commands (like muscle activation) or whether we combine a few muscle synergies or equilibrium points to move a hand, e.g., between two targets. The first hypothesis implies that a planner produces a desired end-effector position for all time points; the second relies on the dynamics of the muscular-skeletal system for a given control command to produce a continuous end-effector trajectory. To distinguish between these two possibilities, we use a visuomotor adaptation experiment. Subjects moved a pen on a graphics tablet and observed the pen's mapped position onto a screen (subjects quickly adapted to this mapping). The task was to move a cursor between two points in a given time window. In the adaptation test, we manipulated the velocity profile of the cursor feedback such that the shape of the trajectories remained unchanged (for straight paths). If humans would use a kinematic plan and map at each time the desired end-effector position onto control commands, subjects should adapt to the above manipulation. In a similar experiment, Wolpert et al (1995) showed adaptation to changes in the curvature of trajectories. This result, however, cannot rule out a shift of an equilibrium point or an additional synergy activation between start and end point of a movement. In our experiment, subjects did two sessions, one control without and one with velocity-profile manipulation. To skew the velocity profile of the cursor trajectory, we added to the current velocity, v, the function 0.8*v*cos(pi + pi*x), where x is the projection of the cursor position onto the start-goal line divided by the distance start to goal (x=0 at the start point). As result, subjects did not adapt to this manipulation: for all subjects, the true hand motion was not significantly modified in a direction consistent with adaptation, despite that the visually presented motion differed significantly from the control motion. One may still argue that this difference in motion was insufficient to be processed visually. Thus, as a control experiment, we replayed control and modified motions to the subjects and asked which of the two motions appeared 'more natural'. Subjects chose the unperturbed motion as more natural significantly better than chance. In summary, for a visuomotor transformation task, the hypothesis of a planned continuous end-effector trajectory predicts adaptation to a modified velocity profile. The current experiment found no adaptation under such transformation.

am

[BibTex]

[BibTex]


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Design and Numerical Modeling of an On-Board Chemical Release Module for Motion Control of Bacteria-Propelled Swimming Micro-Robots

Behkam, B., Nain, A. S., Amon, C. H., Sitti, M.

In ASME 2008 International Mechanical Engineering Congress and Exposition, pages: 239-244, 2008 (inproceedings)

pi

[BibTex]

[BibTex]


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Dynamic modeling of stick slip motion in an untethered magnetic microrobot

Pawashe, C., Floyd, S., Sitti, M.

Proceedings of Robotics: Science and Systems IV, Zurich, Switzerland, 2008 (article)

pi

[BibTex]

[BibTex]


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Investigation of Calcium Mechanotransduction by Quasi 3-D Microfiber Mechanical Stimulation of Cells

Ruder, W. C., Pratt, E. D., Sitti, M., LeDuc, P. R., Antaki, J. F.

In ASME 2008 Summer Bioengineering Conference, pages: 1049-1050, 2008 (inproceedings)

pi

[BibTex]

[BibTex]


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Beanbag robotics: Robotic swarms with 1-dof units

Kriesel, D. M., Cheung, E., Sitti, M., Lipson, H.

In International Conference on Ant Colony Optimization and Swarm Intelligence, pages: 267-274, 2008 (inproceedings)

pi

[BibTex]

[BibTex]


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Particle image velocimetry and thrust of flagellar micro propulsion systems

Danis, U., Sitti, M., Pekkan, K.

In APS Division of Fluid Dynamics Meeting Abstracts, 1, 2008 (inproceedings)

pi

[BibTex]

[BibTex]


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Frequency analysis with coupled nonlinear oscillators

Buchli, J., Righetti, L., Ijspeert, A.

Physica D: Nonlinear Phenomena, 237(13):1705-1718, August 2008 (article)

Abstract
We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronization and adaptation properties of the component oscillators are exploited. The frequency spectrum of the signal is reflected in the statistics of the intrinsic frequencies of the oscillators. The frequency analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the oscillators tune to the correct frequencies for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker–Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence.

mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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A modular bio-inspired architecture for movement generation for the infant-like robot iCub

Degallier, S., Righetti, L., Natale, L., Nori, F., Metta, G., Ijspeert, A.

In 2008 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, pages: 795-800, IEEE, Scottsdale, USA, October 2008 (inproceedings)

Abstract
Movement generation in humans appears to be processed through a three-layered architecture, where each layer corresponds to a different level of abstraction in the representation of the movement. In this article, we will present an architecture reflecting this organization and based on a modular approach to human movement generation. We will show that our architecture is well suited for the online generation and modulation of motor behaviors, but also for switching between motor behaviors. This will be illustrated respectively through an interactive drumming task and through switching between reaching and crawling.

mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Röntgenzirkulardichroische Untersuchungen XMCD an FePt und Ferrit Nanopartikeln

Nolle, D.

Universität Stuttgart, Stuttgart, 2008 (mastersthesis)

mms

[BibTex]

[BibTex]


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Nanostructured biointerfaces for investigating cellular adhesion and differentiation

Gojak, C.

Universität Heidelberg, Heidelberg, 2008 (mastersthesis)

mms

[BibTex]

[BibTex]


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In situ observation of cracks in gold nano-interconnects on flexible substrates

Olliges, S., Gruber, P. A., Orso, S., Auzelyte, V., Ekinci, Y., Solak, H. H., Spolenak, R.

{Scripta Materialia}, 58(3):175-178, 2008 (article)

mms

[BibTex]

[BibTex]


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Transmission electron microscopy study of the intermixing of Fe-Pt multilayers

Kaiser, T., Sigle, W., Goll, D., Goo, N. H., Srot, V., van Aken, P. A., Detemple, E., Jäger, W.

{Journal of Applied Physics}, 103, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Spin state and orbita moments across the metal-insulator-transition of REBaCo2O5.5 investigated by XMCD

Lafkioti, M., Goering, E., Gold, S., Schütz, G., Barilo, S. N., Shiryaev, S. V., Bychkov, G. L., Lemmens, P., Hinkov, V., Deisenhofer, J., Loidl, A.

{New Journal of Physics}, 10, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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A crucial role for primary cilia in cortical morphogenesis

Willaredt, M. A., Hasenpusch-Theil, K., Gardner, H. A. R., Kitanovic, I., Hirschfeld-Warneken, V. C., Gojak, C. P., Gorgas, K., Bradford, C. L., Spatz, J. P., Wölfl, S., Theil, T., Tucker, K. L.

{The Journal of Neuroscience}, 28(48):12887-12900, 2008 (article)

mms

[BibTex]

[BibTex]


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Exchange coupled composite layers for magnetic recording

Goll, D., Macke, S., Kronmüller, H.

{Physica B}, 403, pages: 338-341, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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XMCD studies on Co and Li doped ZnO magnetic semiconductors

Tietze, T., Gacic, M., Schütz, G., Jakob, G., Brück, S., Goering, E.

{New Journal of Physics}, 10, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Desorption studies of hydrogen in metal-organic frameworks

Panella, B., Hönes, K., Müller, U., Trukhan, N., Schubert, M., Pütter, H., Hirscher, M.

{Angewandte Chemie International Edition}, 47, pages: 2138-2142, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Wetting transition of grain-boundary triple junctions

Straumal, B. B., Kogtenkova, O., Zieba, P.

{Acta Materialia}, 56, pages: 925-933, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Time-resolved X-ray microscopy of spin-torque-induced magnetic vortex gyration

Bolte, M., Meier, G., Krüger, B., Drews, A., Eiselt, R., Bocklage, L., Bohlens, S., Tyliszczak, T., Vansteenkiste, A., Van Waeyenberge, B., Chou, K. W., Puzic, A., Stoll, H.

{Physical Review Letters}, 100, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Study of the intermixing of Fe\textendashPt multilayers by analytical and high-resolution transmission electron microscopy

Sigle, W., Kaiser, T., Goll, D., Goo, N. H., Srot, V., van Aken, P. A., Detemple, E., Jäger, W.

In EMC2008, 14th European Microscopy Congress, Vol. 2: Materials Science, pages: 109-110, Springer, Aachen, Germany, 2008 (inproceedings)

mms

DOI [BibTex]

DOI [BibTex]


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The Gilbert equation revisited: anisotropic and nonlocal damping of magnetization dynamics

Fähnle, M., Steiauf, D., Seib, J.

{Journal of Physics D}, 41, 2008 (article)

mms

DOI [BibTex]

DOI [BibTex]

2005


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Kernel Methods for Measuring Independence

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

Journal of Machine Learning Research, 6, pages: 2075-2129, December 2005 (article)

Abstract
We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prove that when the RKHSs are universal, both functionals are zero if and only if the random variables are pairwise independent. We also show that the kernel mutual information is an upper bound near independence on the Parzen window estimate of the mutual information. Analogous results apply for two correlation-based dependence functionals introduced earlier: we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels, and prove the latter to be an upper bound on the mutual information near independence. The performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis.

ei

PDF PostScript PDF [BibTex]

2005


PDF PostScript PDF [BibTex]


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Kernel ICA for Large Scale Problems

Jegelka, S., Gretton, A., Achlioptas, D.

In pages: -, NIPS Workshop on Large Scale Kernel Machines, December 2005 (inproceedings)

ei

Web [BibTex]

Web [BibTex]


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Some thoughts about Gaussian Processes

Chapelle, O.

NIPS Workshop on Open Problems in Gaussian Processes for Machine Learning, December 2005 (talk)

ei

PDF Web [BibTex]

PDF Web [BibTex]


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A Unifying View of Sparse Approximate Gaussian Process Regression

Quinonero Candela, J., Rasmussen, C.

Journal of Machine Learning Research, 6, pages: 1935-1959, December 2005 (article)

Abstract
We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the methods are using. This allows new insights to be gained, and highlights the relationship between existing methods. It also allows for a clear theoretically justified ranking of the closeness of the known approximations to the corresponding full GPs. Finally we point directly to designs of new better sparse approximations, combining the best of the existing strategies, within attractive computational constraints.

ei

PDF [BibTex]

PDF [BibTex]


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Popper, Falsification and the VC-dimension

Corfield, D., Schölkopf, B., Vapnik, V.

(145), Max Planck Institute for Biological Cybernetics, November 2005 (techreport)

ei

PDF [BibTex]

PDF [BibTex]


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Extension to Kernel Dependency Estimation with Applications to Robotics

BakIr, G.

Biologische Kybernetik, Technische Universität Berlin, Berlin, November 2005 (phdthesis)

Abstract
Kernel Dependency Estimation(KDE) is a novel technique which was designed to learn mappings between sets without making assumptions on the type of the involved input and output data. It learns the mapping in two stages. In a first step, it tries to estimate coordinates of a feature space representation of elements of the set by solving a high dimensional multivariate regression problem in feature space. Following this, it tries to reconstruct the original representation given the estimated coordinates. This thesis introduces various algorithmic extensions to both stages in KDE. One of the contributions of this thesis is to propose a novel linear regression algorithm that explores low-dimensional subspaces during learning. Furthermore various existing strategies for reconstructing patterns from feature maps involved in KDE are discussed and novel pre-image techniques are introduced. In particular, pre-image techniques for data-types that are of discrete nature such as graphs and strings are investigated. KDE is then explored in the context of robot pose imitation where the input is a an image with a human operator and the output is the robot articulated variables. Thus, using KDE, robot pose imitation is formulated as a regression problem.

ei

PDF PDF [BibTex]

PDF PDF [BibTex]


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Kernel methods for dependence testing in LFP-MUA

Gretton, A., Belitski, A., Murayama, Y., Schölkopf, B., Logothetis, N.

35(689.17), 35th Annual Meeting of the Society for Neuroscience (Neuroscience), November 2005 (poster)

Abstract
A fundamental problem in neuroscience is determining whether or not particular neural signals are dependent. The correlation is the most straightforward basis for such tests, but considerable work also focuses on the mutual information (MI), which is capable of revealing dependence of higher orders that the correlation cannot detect. That said, there are other measures of dependence that share with the MI an ability to detect dependence of any order, but which can be easier to compute in practice. We focus in particular on tests based on the functional covariance, which derive from work originally accomplished in 1959 by Renyi. Conceptually, our dependence tests work by computing the covariance between (infinite dimensional) vectors of nonlinear mappings of the observations being tested, and then determining whether this covariance is zero - we call this measure the constrained covariance (COCO). When these vectors are members of universal reproducing kernel Hilbert spaces, we can prove this covariance to be zero only when the variables being tested are independent. The greatest advantage of these tests, compared with the mutual information, is their simplicity – when comparing two signals, we need only take the largest eigenvalue (or the trace) of a product of two matrices of nonlinearities, where these matrices are generally much smaller than the number of observations (and are very simple to construct). We compare the mutual information, the COCO, and the correlation in the context of finding changes in dependence between the LFP and MUA signals in the primary visual cortex of the anaesthetized macaque, during the presentation of dynamic natural stimuli. We demonstrate that the MI and COCO reveal dependence which is not detected by the correlation alone (which we prove by artificially removing all correlation between the signals, and then testing their dependence with COCO and the MI); and that COCO and the MI give results consistent with each other on our data.

ei

Web [BibTex]

Web [BibTex]


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Training Support Vector Machines with Multiple Equality Constraints

Kienzle, W., Schölkopf, B.

In Proceedings of the 16th European Conference on Machine Learning, Lecture Notes in Computer Science, Vol. 3720, pages: 182-193, (Editors: JG Carbonell and J Siekmann), Springer, Berlin, Germany, ECML, November 2005 (inproceedings)

Abstract
In this paper we present a primal-dual decomposition algorithm for support vector machine training. As with existing methods that use very small working sets (such as Sequential Minimal Optimization (SMO), Successive Over-Relaxation (SOR) or the Kernel Adatron (KA)), our method scales well, is straightforward to implement, and does not require an external QP solver. Unlike SMO, SOR and KA, the method is applicable to a large number of SVM formulations regardless of the number of equality constraints involved. The effectiveness of our algorithm is demonstrated on a more difficult SVM variant in this respect, namely semi-parametric support vector regression.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


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Geometrical aspects of statistical learning theory

Hein, M.

Biologische Kybernetik, Darmstadt, Darmstadt, November 2005 (phdthesis)

ei

PDF [BibTex]

PDF [BibTex]


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Measuring Statistical Dependence with Hilbert-Schmidt Norms

Gretton, A., Bousquet, O., Smola, A., Schoelkopf, B.

In Algorithmic Learning Theory, Lecture Notes in Computer Science, Vol. 3734, pages: 63-78, (Editors: S Jain and H-U Simon and E Tomita), Springer, Berlin, Germany, 16th International Conference ALT, October 2005 (inproceedings)

Abstract
We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on {methodname} do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


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Maximal Margin Classification for Metric Spaces

Hein, M., Bousquet, O., Schölkopf, B.

Journal of Computer and System Sciences, 71(3):333-359, October 2005 (article)

Abstract
In order to apply the maximum margin method in arbitrary metric spaces, we suggest to embed the metric space into a Banach or Hilbert space and to perform linear classification in this space. We propose several embeddings and recall that an isometric embedding in a Banach space is always possible while an isometric embedding in a Hilbert space is only possible for certain metric spaces. As a result, we obtain a general maximum margin classification algorithm for arbitrary metric spaces (whose solution is approximated by an algorithm of Graepel. Interestingly enough, the embedding approach, when applied to a metric which can be embedded into a Hilbert space, yields the SVM algorithm, which emphasizes the fact that its solution depends on the metric and not on the kernel. Furthermore we give upper bounds of the capacity of the function classes corresponding to both embeddings in terms of Rademacher averages. Finally we compare the capacities of these function classes directly.

ei

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]