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A 32-channel multi-coil setup optimized for human brain shimming at 9.4T

Aghaeifar, A., Zhou, J., Heule, R., Tabibian, B., Schölkopf, B., Jia, F., Zaitsev, M., Scheffler, K.

Magnetic Resonance in Medicine, 2019, (Early View) (article)

DOI [BibTex]

DOI [BibTex]


Multidimensional Contrast Limited Adaptive Histogram Equalization
Multidimensional Contrast Limited Adaptive Histogram Equalization

Stimper, V., Bauer, S., Ernstorfer, R., Schölkopf, B., Xian, R. P.

IEEE Access, 7, pages: 165437-165447, 2019 (article)

arXiv link (url) DOI [BibTex]

arXiv link (url) DOI [BibTex]


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Enhancing Human Learning via Spaced Repetition Optimization

Tabibian, B., Upadhyay, U., De, A., Zarezade, A., Schölkopf, B., Gomez Rodriguez, M.

Proceedings of the National Academy of Sciences, 2019, PNAS published ahead of print January 22, 2019 (article)

DOI Project Page Project Page [BibTex]

DOI Project Page Project Page [BibTex]


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Spatial Filtering based on Riemannian Manifold for Brain-Computer Interfacing

Xu, J.

Technical University of Munich, Germany, 2019 (mastersthesis)

[BibTex]

[BibTex]


Learning to Control Highly Accelerated Ballistic Movements on Muscular Robots
Learning to Control Highly Accelerated Ballistic Movements on Muscular Robots

Büchler, D., Calandra, R., Peters, J.

2019 (article) Submitted

Abstract
High-speed and high-acceleration movements are inherently hard to control. Applying learning to the control of such motions on anthropomorphic robot arms can improve the accuracy of the control but might damage the system. The inherent exploration of learning approaches can lead to instabilities and the robot reaching joint limits at high speeds. Having hardware that enables safe exploration of high-speed and high-acceleration movements is therefore desirable. To address this issue, we propose to use robots actuated by Pneumatic Artificial Muscles (PAMs). In this paper, we present a four degrees of freedom (DoFs) robot arm that reaches high joint angle accelerations of up to 28000 °/s^2 while avoiding dangerous joint limits thanks to the antagonistic actuation and limits on the air pressure ranges. With this robot arm, we are able to tune control parameters using Bayesian optimization directly on the hardware without additional safety considerations. The achieved tracking performance on a fast trajectory exceeds previous results on comparable PAM-driven robots. We also show that our system can be controlled well on slow trajectories with PID controllers due to careful construction considerations such as minimal bending of cables, lightweight kinematics and minimal contact between PAMs and PAMs with the links. Finally, we propose a novel technique to control the the co-contraction of antagonistic muscle pairs. Experimental results illustrate that choosing the optimal co-contraction level is vital to reach better tracking performance. Through the use of PAM-driven robots and learning, we do a small step towards the future development of robots capable of more human-like motions.

Arxiv Video [BibTex]


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AReS and MaRS Adversarial and MMD-Minimizing Regression for SDEs

Abbati*, G., Wenk*, P., Osborne, M. A., Krause, A., Schölkopf, B., Bauer, S.

Proceedings of the 36th International Conference on Machine Learning (ICML), 97, pages: 1-10, Proceedings of Machine Learning Research, (Editors: Chaudhuri, Kamalika and Salakhutdinov, Ruslan), PMLR, 2019, *equal contribution (conference)

PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Perception of temporal dependencies in autoregressive motion

Meding, K., Schölkopf, B., Wichmann, F. A.

European Conference on Visual Perception (ECVP), 2019 (poster)

[BibTex]


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Inferring causation from time series with perspectives in Earth system sciences

Runge, J., Bathiany, S., Bollt, E., Camps-Valls, G., Coumou, D., Deyle, E., Glymour, C., Kretschmer, M., Mahecha, M., van Nes, E., Peters, J., Quax, R., Reichstein, M., Scheffer, M. S. B., Spirtes, P., Sugihara, G., Sun, J., Zhang, K., Zscheischler, J.

Nature Communications, 2019 (article) In revision

[BibTex]

[BibTex]


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Quantum mean embedding of probability distributions

Kübler, J. M., Muandet, K., Schölkopf, B.

Physical Review Research, 1(3):033159, American Physical Society, 2019 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Quantification of tumor heterogeneity using PET/MRI and machine learning

Katiyar, P.

Eberhard Karls Universität Tübingen, Germany, 2019 (phdthesis)

[BibTex]

[BibTex]


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MYND: A Platform for Large-scale Neuroscientific Studies

Hohmann, M. R., Hackl, M., Wirth, B., Zaman, T., Enficiaud, R., Grosse-Wentrup, M., Schölkopf, B.

Proceedings of the 2019 Conference on Human Factors in Computing Systems (CHI), 2019 (conference) Accepted

[BibTex]

[BibTex]


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A Kernel Stein Test for Comparing Latent Variable Models

Kanagawa, H., Jitkrittum, W., Mackey, L., Fukumizu, K., Gretton, A.

2019 (conference) Submitted

arXiv [BibTex]

arXiv [BibTex]


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Phenomenal Causality and Sensory Realism

Bruijns, S. A., Meding, K., Schölkopf, B., Wichmann, F. A.

European Conference on Visual Perception (ECVP), 2019 (poster)

[BibTex]

[BibTex]


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Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces

Klus, S., Schuster, I., Muandet, K.

Journal of Nonlinear Science, 2019, First Online: 21 August 2019 (article)

DOI [BibTex]

DOI [BibTex]

2007


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HPLC analysis and pharmacokinetic study of quercitrin and isoquercitrin in rat plasma after administration of Hypericum japonicum thunb. extract.

Li, J., Wang, W., Zhang, L., Chen, H., Bi, S.

Biomedical Chromatography, 22(4):374-378, December 2007 (article)

Abstract
A simple HPLC method was developed for determination of quercitrin and isoquercitrin in rat plasma. Reversed-phase HPLC was employed for the quantitative analysis using kaempferol-3-O--d-glucopyranoside-7-O--l-rhamnoside as an internal standard. Following extraction from the plasma samples with ethyl acetate-isopropanol (95:5, v/v), these two compounds were successfully separated on a Luna C18 column (250 × 4.6 mm, 5 µm) with isocratic elution of acetonitrile-0.5% aqueous acetic acid (17:83, v/v) as the mobile phase. The flow-rate was set at 1 mL/min and the eluent was detected at 350 nm for both quercitrin and isoquercitrin. The method was linear over the studied ranges of 50-6000 and 50-5000 ng/mL for quercitrin and isoquercitrin, respectively. The intra- and inter-day precisions of the analysis were better than 13.1 and 13.2%, respectively. The lower limits of quantitation for quercitrin and isoquercitrin in plasma were both of 50 ng/mL. The mean extraction recoveries were 73 and 61% for quercitrin and i soquercitrin, respectively. The validated method was successfully applied to pharmacokinetic studies of the two analytes in rat plasma after the oral administration of Hypericum japonicum thunb. ethanol extract.

Web DOI [BibTex]


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Reaction graph kernels for discovering missing enzymes in the plant secondary metabolism

Saigo, H., Hattori, M., Tsuda, K.

NIPS Workshop on Machine Learning in Computational Biology, December 2007 (talk)

Abstract
Secondary metabolic pathway in plant is important for finding druggable candidate enzymes. However, there are many enzymes whose functions are still undiscovered especially in organism-specific metabolic pathways. We propose reaction graph kernels for automatically assigning the EC numbers to unknown enzymatic reactions in a metabolic network. Experiments are carried out on KEGG/REACTION database and our method successfully predicted the first three digits of the EC number with 83% accuracy.We also exhaustively predicted missing enzymatic functions in the plant secondary metabolism pathways, and evaluated our results in biochemical validity.

Web [BibTex]

Web [BibTex]


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Positional Oligomer Importance Matrices

Sonnenburg, S., Zien, A., Philips, P., Rätsch, G.

NIPS Workshop on Machine Learning in Computational Biology, December 2007 (talk)

Abstract
At the heart of many important bioinformatics problems, such as gene finding and function prediction, is the classification of biological sequences, above all of DNA and proteins. In many cases, the most accurate classifiers are obtained by training SVMs with complex sequence kernels, for instance for transcription starts or splice sites. However, an often criticized downside of SVMs with complex kernels is that it is very hard for humans to understand the learned decision rules and to derive biological insights from them. To close this gap, we introduce the concept of positional oligomer importance matrices (POIMs) and develop an efficient algorithm for their computation. We demonstrate how they overcome the limitations of sequence logos, and how they can be used to find relevant motifs for different biological phenomena in a straight-forward way. Note that the concept of POIMs is not limited to interpreting SVMs, but is applicable to general k−mer based scoring systems.

Web [BibTex]

Web [BibTex]


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Machine Learning Algorithms for Polymorphism Detection

Schweikert, G., Zeller, G., Weigel, D., Schölkopf, B., Rätsch, G.

NIPS Workshop on Machine Learning in Computational Biology, December 2007 (talk)

Web [BibTex]

Web [BibTex]


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Graph sharpening plus graph integration: a synergy that improves protein functional classification

Shin, HH., Lisewski, AM., Lichtarge, O.

Bioinformatics, 23(23):3217-3224, December 2007 (article)

Web DOI [BibTex]

Web DOI [BibTex]


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A Tutorial on Spectral Clustering

von Luxburg, U.

Statistics and Computing, 17(4):395-416, December 2007 (article)

Abstract
In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


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An Automated Combination of Kernels for Predicting Protein Subcellular Localization

Zien, A., Ong, C.

NIPS Workshop on Machine Learning in Computational Biology, December 2007 (talk)

Abstract
Protein subcellular localization is a crucial ingredient to many important inferences about cellular processes, including prediction of protein function and protein interactions.We propose a new class of protein sequence kernels which considers all motifs including motifs with gaps. This class of kernels allows the inclusion of pairwise amino acid distances into their computation. We utilize an extension of the multiclass support vector machine (SVM)method which directly solves protein subcellular localization without resorting to the common approach of splitting the problem into several binary classification problems. To automatically search over families of possible amino acid motifs, we optimize over multiple kernels at the same time. We compare our automated approach to four other predictors on three different datasets, and show that we perform better than the current state of the art. Furthermore, our method provides some insights as to which features are most useful for determining subcellular localization, which are in agreement with biological reasoning.

Web [BibTex]

Web [BibTex]


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A Tutorial on Kernel Methods for Categorization

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

Journal of Mathematical Psychology, 51(6):343-358, December 2007 (article)

Abstract
The abilities to learn and to categorize are fundamental for cognitive systems, be it animals or machines, and therefore have attracted attention from engineers and psychologists alike. Modern machine learning methods and psychological models of categorization are remarkably similar, partly because these two fields share a common history in artificial neural networks and reinforcement learning. However, machine learning is now an independent and mature field that has moved beyond psychologically or neurally inspired algorithms towards providing foundations for a theory of learning that is rooted in statistics and functional analysis. Much of this research is potentially interesting for psychological theories of learning and categorization but also hardly accessible for psychologists. Here, we provide a tutorial introduction to a popular class of machine learning tools, called kernel methods. These methods are closely related to perceptrons, radial-basis-function neural networks and exemplar theories of catego rization. Recent theoretical advances in machine learning are closely tied to the idea that the similarity of patterns can be encapsulated in a positive definite kernel. Such a positive definite kernel can define a reproducing kernel Hilbert space which allows one to use powerful tools from functional analysis for the analysis of learning algorithms. We give basic explanations of some key concepts—the so-called kernel trick, the representer theorem and regularization—which may open up the possibility that insights from machine learning can feed back into psychology.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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A semigroup approach to queueing systems

Haji, A., Radl, A.

Semigroup Forum, 75(3):610-624, December 2007 (article)

Abstract
We prove asymptotic stability of the solutions of equations describing a simple queueing system consisting of two machines separated by a finite storage buffer. Following an approach by G. Gupur, we apply the theory of C0-semigroups and spectral theory of positive operators.

PDF DOI [BibTex]

PDF DOI [BibTex]


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Point-spread functions for backscattered imaging in the scanning electron microscope

Hennig, P., Denk, W.

Journal of Applied Physics , 102(12):1-8, December 2007 (article)

Abstract
One knows the imaging system's properties are central to the correct interpretation of any image. In a scanning electron microscope regions of different composition generally interact in a highly nonlinear way during signal generation. Using Monte Carlo simulations we found that in resin-embedded, heavy metal-stained biological specimens staining is sufficiently dilute to allow an approximately linear treatment. We then mapped point-spread functions for backscattered-electron contrast, for primary energies of 3 and 7 keV and for different detector specifications. The point-spread functions are surprisingly well confined (both laterally and in depth) compared even to the distribution of only those scattered electrons that leave the sample again.

Web DOI [BibTex]

Web DOI [BibTex]


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Accurate Splice site Prediction Using Support Vector Machines

Sonnenburg, S., Schweikert, G., Philips, P., Behr, J., Rätsch, G.

BMC Bioinformatics, 8(Supplement 10):1-16, December 2007 (article)

Abstract
Background: For splice site recognition, one has to solve two classification problems: discriminating true from decoy splice sites for both acceptor and donor sites. Gene finding systems typically rely on Markov Chains to solve these tasks. Results: In this work we consider Support Vector Machines for splice site recognition. We employ the so-called weighted degree kernel which turns out well suited for this task, as we will illustrate in several experiments where we compare its prediction accuracy with that of recently proposed systems. We apply our method to the genome-wide recognition of splice sites in Caenorhabditis elegans, Drosophila melanogaster, Arabidopsis thaliana, Danio rerio, and Homo sapiens. Our performance estimates indicate that splice sites can be recognized very accurately in these genomes and that our method outperforms many other methods including Markov Chains, GeneSplicer and SpliceMachine. We provide genome-wide predictions of splice sites and a stand-alone prediction tool ready to be used for incorporation in a gene finder. Availability: Data, splits, additional information on the model selection, the whole genome predictions, as well as the stand-alone prediction tool are available for download at http:// www.fml.mpg.de/raetsch/projects/splice.

PDF DOI [BibTex]

PDF DOI [BibTex]


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Challenges in Brain-Computer Interface Development: Induction, Measurement, Decoding, Integration

Hill, NJ.

Invited keynote talk at the launch of BrainGain, the Dutch BCI research consortium, November 2007 (talk)

Abstract
I‘ll present a perspective on Brain-Computer Interface development from T{\"u}bingen. Some of the benefits promised by BCI technology lie in the near foreseeable future, and some further away. Our motivation is to make BCI technology feasible for the people who could benefit from what it has to offer soon: namely, people in the "completely locked-in" state. I‘ll mention some of the challenges of working with this user group, and explain the specific directions they have motivated us to take in developing experimental methods, algorithms, and software.

[BibTex]

[BibTex]


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Towards compliant humanoids: an experimental assessment of suitable task space position/orientation controllers

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

In IROS 2007, 2007, pages: 2520-2527, (Editors: Grant, E. , T. C. Henderson), IEEE Service Center, Piscataway, NJ, USA, IEEE/RSJ International Conference on Intelligent Robots and Systems, November 2007 (inproceedings)

Abstract
Compliant control will be a prerequisite for humanoid robotics if these robots are supposed to work safely and robustly in human and/or dynamic environments. One view of compliant control is that a robot should control a minimal number of degrees-of-freedom (DOFs) directly, i.e., those relevant DOFs for the task, and keep the remaining DOFs maximally compliant, usually in the null space of the task. This view naturally leads to task space control. However, surprisingly few implementations of task space control can be found in actual humanoid robots. This paper makes a first step towards assessing the usefulness of task space controllers for humanoids by investigating which choices of controllers are available and what inherent control characteristics they have—this treatment will concern position and orientation control, where the latter is based on a quaternion formulation. Empirical evaluations on an anthropomorphic Sarcos master arm illustrate the robustness of the different controllers as well as the eas e of implementing and tuning them. Our extensive empirical results demonstrate that simpler task space controllers, e.g., classical resolved motion rate control or resolved acceleration control can be quite advantageous in face of inevitable modeling errors in model-based control, and that well chosen formulations are easy to implement and quite robust, such that they are useful for humanoids.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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MR-Based PET Attenuation Correction: Method and Validation

Hofmann, M., Steinke, F., Scheel, V., Charpiat, G., Brady, M., Schölkopf, B., Pichler, B.

2007 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC 2007), 2007(M16-6):1-2, November 2007 (poster)

Abstract
PET/MR combines the high soft tissue contrast of Magnetic Resonance Imaging (MRI) and the functional information of Positron Emission Tomography (PET). For quantitative PET information, correction of tissue photon attenuation is mandatory. Usually in conventional PET, the attenuation map is obtained from a transmission scan, which uses a rotating source, or from the CT scan in case of combined PET/CT. In the case of a PET/MR scanner, there is insufficient space for the rotating source and ideally one would want to calculate the attenuation map from the MR image instead. Since MR images provide information about proton density of the different tissue types, it is not trivial to use this data for PET attenuation correction. We present a method for predicting the PET attenuation map from a given the MR image, using a combination of atlas-registration and recognition of local patterns. Using "leave one out cross validation" we show on a database of 16 MR-CT image pairs that our method reliably allows estimating the CT image from the MR image. Subsequently, as in PET/CT, the PET attenuation map can be predicted from the CT image. On an additional dataset of MR/CT/PET triplets we quantitatively validate that our approach allows PET quantification with an error that is smaller than what would be clinically significant. We demonstrate our approach on T1-weighted human brain scans. However, the presented methods are more general and current research focuses on applying the established methods to human whole body PET/MRI applications.

PDF PDF [BibTex]

PDF PDF [BibTex]


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Estimating receptive fields without spike-triggering

Macke, J., Zeck, G., Bethge, M.

37th annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37(768.1):1, November 2007 (poster)

Web [BibTex]

Web [BibTex]


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Sistema avanzato per la classificazione delle aree agricole in immagini ad elevata risoluzione geometrica: applicazione al territorio del Trentino

Arnoldi, E., Bruzzone, L., Carlin, L., Pedron, L., Persello, C.

In pages: 1-6, 11. Conferenza Nazionale ASITA, November 2007 (inproceedings)

PDF Web [BibTex]

PDF Web [BibTex]


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Evaluation of Deformable Registration Methods for MR-CT Atlas Alignment

Scheel, V., Hofmann, M., Rehfeld, N., Judenhofer, M., Claussen, C., Pichler, B.

2007 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC 2007), 2007(M13-121):1, November 2007 (poster)

Abstract
Deformable registration methods are essential for multimodality imaging. Many different methods exist but due to the complexity of the deformed images a direct comparison of the methods is difficult. One particular application that requires high accuracy registration of MR-CT images is atlas-based attenuation correction for PET/MR. We compare four deformable registration algorithms for 3D image data included in the Open Source "National Library of Medicine Insight Segmentation and Registration Toolkit" (ITK). An interactive landmark based registration using MiraView (Siemens) has been used as gold standard. The automatic algorithms provided by ITK are based on the metrics Mattes mutual information as well as on normalized mutual information. The transformations are calculated by interpolating over a uniform B-Spline grid laying over the image to be warped. The algorithms were tested on head images from 10 subjects. We implemented a measure which segments head interior bone and air based on the CT images and l ow intensity classes of corresponding MRI images. The segmentation of bone is performed by individually calculating the lowest Hounsfield unit threshold for each CT image. The compromise is made by quantifying the number of overlapping voxels of the remaining structures. We show that the algorithms provided by ITK achieve similar or better accuracy than the time-consuming interactive landmark based registration. Thus, ITK provides an ideal platform to generate accurately fused datasets from different modalities, required for example for building training datasets for Atlas-based attenuation correction.

PDF [BibTex]

PDF [BibTex]


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Some Theoretical Aspects of Human Categorization Behavior: Similarity and Generalization

Jäkel, F.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, November 2007, passed with "ausgezeichnet", summa cum laude, published online (phdthesis)

PDF [BibTex]

PDF [BibTex]


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Statistical Learning Theory Approaches to Clustering

Jegelka, S.

Biologische Kybernetik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany, November 2007 (diplomathesis)

PDF [BibTex]

PDF [BibTex]


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Performance Stabilization and Improvement in Graph-based Semi-supervised Learning with Ensemble Method and Graph Sharpening

Choi, I., Shin, H.

In Korean Data Mining Society Conference, pages: 257-262, Korean Data Mining Society, Seoul, Korea, Korean Data Mining Society Conference, November 2007 (inproceedings)

PDF [BibTex]

PDF [BibTex]


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A time/frequency decomposition of information transmission by LFPs and spikes in the primary visual cortex

Belitski, A., Gretton, A., Magri, C., Murayama, Y., Montemurro, M., Logothetis, N., Panzeri, S.

37th Annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37, pages: 1, November 2007 (poster)

Web [BibTex]

Web [BibTex]


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Mining expression-dependent modules in the human interaction network

Georgii, E., Dietmann, S., Uno, T., Pagel, P., Tsuda, K.

BMC Bioinformatics, 8(Suppl. 8):S4, November 2007 (poster)

PDF DOI [BibTex]

PDF DOI [BibTex]


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Policy Learning for Robotics

Peters, J.

14th International Conference on Neural Information Processing (ICONIP), November 2007 (talk)

Web [BibTex]

Web [BibTex]


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A unifying framework for robot control with redundant DOFs

Peters, J., Mistry, M., Udwadia, F., Nakanishi, J., Schaal, S.

Autonomous Robots, 24(1):1-12, October 2007 (article)

Abstract
Recently, Udwadia (Proc. R. Soc. Lond. A 2003:1783–1800, 2003) suggested to derive tracking controllers for mechanical systems with redundant degrees-of-freedom (DOFs) using a generalization of Gauss’ principle of least constraint. This method allows reformulating control problems as a special class of optimal controllers. In this paper, we take this line of reasoning one step further and demonstrate that several well-known and also novel nonlinear robot control laws can be derived from this generic methodology. We show experimental verifications on a Sarcos Master Arm robot for some of the derived controllers. The suggested approach offers a promising unification and simplification of nonlinear control law design for robots obeying rigid body dynamics equations, both with or without external constraints, with over-actuation or underactuation, as well as open-chain and closed-chain kinematics.

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


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The Need for Open Source Software in Machine Learning

Sonnenburg, S., Braun, M., Ong, C., Bengio, S., Bottou, L., Holmes, G., LeCun, Y., Müller, K., Pereira, F., Rasmussen, C., Rätsch, G., Schölkopf, B., Smola, A., Vincent, P., Weston, J., Williamson, R.

Journal of Machine Learning Research, 8, pages: 2443-2466, October 2007 (article)

Abstract
Open source tools have recently reached a level of maturity which makes them suitable for building large-scale real-world systems. At the same time, the field of machine learning has developed a large body of powerful learning algorithms for diverse applications. However, the true potential of these methods is not realized, since existing implementations are not openly shared, resulting in software with low usability, and weak interoperability. We argue that this situation can be significantly improved by increasing incentives for researchers to publish their software under an open source model. Additionally, we outline the problems authors are faced with when trying to publish algorithmic implementations of machine learning methods. We believe that a resource of peer reviewed software accompanied by short articles would be highly valuable to both the machine learning and the general scientific community.

PDF Web [BibTex]

PDF Web [BibTex]


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Hilbert Space Representations of Probability Distributions

Gretton, A.

2nd Workshop on Machine Learning and Optimization at the ISM, October 2007 (talk)

Abstract
Many problems in unsupervised learning require the analysis of features of probability distributions. At the most fundamental level, we might wish to determine whether two distributions are the same, based on samples from each - this is known as the two-sample or homogeneity problem. We use kernel methods to address this problem, by mapping probability distributions to elements in a reproducing kernel Hilbert space (RKHS). Given a sufficiently rich RKHS, these representations are unique: thus comparing feature space representations allows us to compare distributions without ambiguity. Applications include testing whether cancer subtypes are distinguishable on the basis of DNA microarray data, and whether low frequency oscillations measured at an electrode in the cortex have a different distribution during a neural spike. A more difficult problem is to discover whether two random variables drawn from a joint distribution are independent. It turns out that any dependence between pairs of random variables can be encoded in a cross-covariance operator between appropriate RKHS representations of the variables, and we may test independence by looking at a norm of the operator. We demonstrate this independence test by establishing dependence between an English text and its French translation, as opposed to French text on the same topic but otherwise unrelated. Finally, we show that this operator norm is itself a difference in feature means.

PDF Web [BibTex]

PDF Web [BibTex]