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2017


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Generalized exploration in policy search

van Hoof, H., Tanneberg, D., Peters, J.

Machine Learning, 106(9-10):1705-1724 , (Editors: Kurt Driessens, Dragi Kocev, Marko Robnik‐Sikonja, and Myra Spiliopoulou), October 2017, Special Issue of the ECML PKDD 2017 Journal Track (article)

DOI Project Page [BibTex]

2017

DOI Project Page [BibTex]


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Probabilistic Prioritization of Movement Primitives

Paraschos, A., Lioutikov, R., Peters, J., Neumann, G.

Proceedings of the International Conference on Intelligent Robot Systems, and IEEE Robotics and Automation Letters (RA-L), 2(4):2294-2301, October 2017 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Movement Primitive Libraries through Probabilistic Segmentation

Lioutikov, R., Neumann, G., Maeda, G., Peters, J.

International Journal of Robotics Research, 36(8):879-894, July 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Guiding Trajectory Optimization by Demonstrated Distributions

Osa, T., Ghalamzan E., A. M., Stolkin, R., Lioutikov, R., Peters, J., Neumann, G.

IEEE Robotics and Automation Letters, 2(2):819-826, April 2017 (article)

DOI [BibTex]

DOI [BibTex]


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Whole-body multi-contact motion in humans and humanoids: Advances of the CoDyCo European project

Padois, V., Ivaldi, S., Babic, J., Mistry, M., Peters, J., Nori, F.

Robotics and Autonomous Systems, 90, pages: 97-117, April 2017, Special Issue on New Research Frontiers for Intelligent Autonomous Systems (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Probabilistic Movement Primitives for Coordination of Multiple Human-Robot Collaborative Tasks

Maeda, G., Neumann, G., Ewerton, M., Lioutikov, R., Kroemer, O., Peters, J.

Autonomous Robots, 41(3):593-612, March 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Bioinspired tactile sensor for surface roughness discrimination

Yi, Z., Zhang, Y., Peters, J.

Sensors and Actuators A: Physical, 255, pages: 46-53, March 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Model-based Contextual Policy Search for Data-Efficient Generalization of Robot Skills

Kupcsik, A., Deisenroth, M., Peters, J., Ai Poh, L., Vadakkepat, V., Neumann, G.

Artificial Intelligence, 247, pages: 415-439, 2017, Special Issue on AI and Robotics (article)

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Anticipatory Action Selection for Human-Robot Table Tennis

Wang, Z., Boularias, A., Mülling, K., Schölkopf, B., Peters, J.

Artificial Intelligence, 247, pages: 399-414, 2017, Special Issue on AI and Robotics (article)

Abstract
Abstract Anticipation can enhance the capability of a robot in its interaction with humans, where the robot predicts the humans' intention for selecting its own action. We present a novel framework of anticipatory action selection for human-robot interaction, which is capable to handle nonlinear and stochastic human behaviors such as table tennis strokes and allows the robot to choose the optimal action based on prediction of the human partner's intention with uncertainty. The presented framework is generic and can be used in many human-robot interaction scenarios, for example, in navigation and human-robot co-manipulation. In this article, we conduct a case study on human-robot table tennis. Due to the limited amount of time for executing hitting movements, a robot usually needs to initiate its hitting movement before the opponent hits the ball, which requires the robot to be anticipatory based on visual observation of the opponent's movement. Previous work on Intention-Driven Dynamics Models (IDDM) allowed the robot to predict the intended target of the opponent. In this article, we address the problem of action selection and optimal timing for initiating a chosen action by formulating the anticipatory action selection as a Partially Observable Markov Decision Process (POMDP), where the transition and observation are modeled by the \{IDDM\} framework. We present two approaches to anticipatory action selection based on the \{POMDP\} formulation, i.e., a model-free policy learning method based on Least-Squares Policy Iteration (LSPI) that employs the \{IDDM\} for belief updates, and a model-based Monte-Carlo Planning (MCP) method, which benefits from the transition and observation model by the IDDM. Experimental results using real data in a simulated environment show the importance of anticipatory action selection, and that \{POMDPs\} are suitable to formulate the anticipatory action selection problem by taking into account the uncertainties in prediction. We also show that existing algorithms for POMDPs, such as \{LSPI\} and MCP, can be applied to substantially improve the robot's performance in its interaction with humans.

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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easyGWAS: A Cloud-based Platform for Comparing the Results of Genome-wide Association Studies

Grimm, D., Roqueiro, D., Salome, P., Kleeberger, S., Greshake, B., Zhu, W., Liu, C., Lippert, C., Stegle, O., Schölkopf, B., Weigel, D., Borgwardt, K.

The Plant Cell, 29(1):5-19, 2017 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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A Novel Unsupervised Segmentation Approach Quantifies Tumor Tissue Populations Using Multiparametric MRI: First Results with Histological Validation

Katiyar, P., Divine, M. R., Kohlhofer, U., Quintanilla-Martinez, L., Schölkopf, B., Pichler, B. J., Disselhorst, J. A.

Molecular Imaging and Biology, 19(3):391-397, 2017 (article)

DOI [BibTex]

DOI [BibTex]


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Minimax Estimation of Kernel Mean Embeddings

Tolstikhin, I., Sriperumbudur, B., Muandet, K.

Journal of Machine Learning Research, 18(86):1-47, 2017 (article)

link (url) Project Page [BibTex]


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Kernel Mean Embedding of Distributions: A Review and Beyond

Muandet, K., Fukumizu, K., Sriperumbudur, B., Schölkopf, B.

Foundations and Trends in Machine Learning, 10(1-2):1-141, 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Prediction of intention during interaction with iCub with Probabilistic Movement Primitives

Dermy, O., Paraschos, A., Ewerton, M., Charpillet, F., Peters, J., Ivaldi, S.

Frontiers in Robotics and AI, 4, pages: 45, 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Manifold-based multi-objective policy search with sample reuse

Parisi, S., Pirotta, M., Peters, J.

Neurocomputing, 263, pages: 3-14, (Editors: Madalina Drugan, Marco Wiering, Peter Vamplew, and Madhu Chetty), 2017, Special Issue on Multi-Objective Reinforcement Learning (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Spectral Clustering predicts tumor tissue heterogeneity using dynamic 18F-FDG PET: a complement to the standard compartmental modeling approach

Katiyar, P., Divine, M. R., Kohlhofer, U., Quintanilla-Martinez, L., Schölkopf, B., Pichler, B. J., Disselhorst, J. A.

Journal of Nuclear Medicine, 58(4):651-657, 2017 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Electroencephalographic identifiers of motor adaptation learning

Ozdenizci, O., Yalcin, M., Erdogan, A., Patoglu, V., Grosse-Wentrup, M., Cetin, M.

Journal of Neural Engineering, 14(4):046027, 2017 (article)

link (url) [BibTex]

link (url) [BibTex]


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Detecting distortions of peripherally presented letter stimuli under crowded conditions

Wallis, T. S. A., Tobias, S., Bethge, M., Wichmann, F. A.

Attention, Perception, & Psychophysics, 79(3):850-862, 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Temporal evolution of the central fixation bias in scene viewing

Rothkegel, L. O. M., Trukenbrod, H. A., Schütt, H. H., Wichmann, F. A., Engbert, R.

Journal of Vision, 17(13):3, 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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BundleMAP: Anatomically Localized Classification, Regression, and Hypothesis Testing in Diffusion MRI

Khatami, M., Schmidt-Wilcke, T., Sundgren, P. C., Abbasloo, A., Schölkopf, B., Schultz, T.

Pattern Recognition, 63, pages: 593-600, 2017 (article)

DOI [BibTex]

DOI [BibTex]


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A parametric texture model based on deep convolutional features closely matches texture appearance for humans

Wallis, T. S. A., Funke, C. M., Ecker, A. S., Gatys, L. A., Wichmann, F. A., Bethge, M.

Journal of Vision, 17(12), 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Model Selection for Gaussian Mixture Models

Huang, T., Peng, H., Zhang, K.

Statistica Sinica, 27(1):147-169, 2017 (article)

link (url) [BibTex]

link (url) [BibTex]


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An image-computable psychophysical spatial vision model

Schütt, H. H., Wichmann, F. A.

Journal of Vision, 17(12), 2017 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Methods and measurements to compare men against machines

Wichmann, F. A., Janssen, D. H. J., Geirhos, R., Aguilar, G., Schütt, H. H., Maertens, M., Bethge, M.

Electronic Imaging, pages: 36-45(10), 2017 (article)

DOI [BibTex]

DOI [BibTex]


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A Comparison of Autoregressive Hidden Markov Models for Multimodal Manipulations With Variable Masses

Kroemer, O., Peters, J.

IEEE Robotics and Automation Letters, 2(2):1101-1108, 2017 (article)

DOI [BibTex]

DOI [BibTex]


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Phase Estimation for Fast Action Recognition and Trajectory Generation in Human-Robot Collaboration

Maeda, G., Ewerton, M., Neumann, G., Lioutikov, R., Peters, J.

International Journal of Robotics Research, 36(13-14):1579-1594, 2017, Special Issue on the Seventeenth International Symposium on Robotics Research (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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A Phase-coded Aperture Camera with Programmable Optics

Chen, J., Hirsch, M., Heintzmann, R., Eberhardt, B., Lensch, H. P. A.

Electronic Imaging, 2017(17):70-75, 2017 (article)

DOI [BibTex]

DOI [BibTex]


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On Maximum Entropy and Inference

Gresele, L., Marsili, M.

Entropy, 19(12):article no. 642, 2017 (article)

link (url) [BibTex]

link (url) [BibTex]


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Towards Engagement Models that Consider Individual Factors in HRI: On the Relation of Extroversion and Negative Attitude Towards Robots to Gaze and Speech During a Human-Robot Assembly Task

Ivaldi, S., Lefort, S., Peters, J., Chetouani, M., Provasi, J., Zibetti, E.

International Journal of Social Robotics, 9(1):63-86, 2017 (article)

DOI [BibTex]


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Non-parametric Policy Search with Limited Information Loss

van Hoof, H., Neumann, G., Peters, J.

Journal of Machine Learning Research , 18(73):1-46, 2017 (article)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Stability of Controllers for Gaussian Process Dynamics

Vinogradska, J., Bischoff, B., Nguyen-Tuong, D., Peters, J.

Journal of Machine Learning Research, 18(100):1-37, 2017 (article)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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SUV-quantification of physiological lung tissue in an integrated PET/MR-system: Impact of lung density and bone tissue

Seith, F., Schmidt, H., Gatidis, S., Bezrukov, I., Schraml, C., Pfannenberg, C., la Fougère, C., Nikolaou, K., Schwenzer, N.

PLOS ONE, 12(5):1-13, 2017 (article)

DOI [BibTex]

DOI [BibTex]

2012


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Jensen-Bregman LogDet Divergence with Application to Efficient Similarity Search for Covariance Matrices

Cherian, A., Sra, S., Banerjee, A., Papanikolopoulos, N.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(9):2161-2174, December 2012 (article)

DOI [BibTex]

2012

DOI [BibTex]


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Hippocampal-Cortical Interaction during Periods of Subcortical Silence

Logothetis, N., Eschenko, O., Murayama, Y., Augath, M., Steudel, T., Evrard, H., Besserve, M., Oeltermann, A.

Nature, 491, pages: 547-553, November 2012 (article)

Abstract
Hippocampal ripples, episodic high-frequency field-potential oscillations primarily occurring during sleep and calmness, have been described in mice, rats, rabbits, monkeys and humans, and so far they have been associated with retention of previously acquired awake experience. Although hippocampal ripples have been studied in detail using neurophysiological methods, the global effects of ripples on the entire brain remain elusive, primarily owing to a lack of methodologies permitting concurrent hippocampal recordings and whole-brain activity mapping. By combining electrophysiological recordings in hippocampus with ripple-triggered functional magnetic resonance imaging, here we show that most of the cerebral cortex is selectively activated during the ripples, whereas most diencephalic, midbrain and brainstem regions are strongly and consistently inhibited. Analysis of regional temporal response patterns indicates that thalamic activity suppression precedes the hippocampal population burst, which itself is temporally bounded by massive activations of association and primary cortical areas. These findings suggest that during off-line memory consolidation, synergistic thalamocortical activity may be orchestrating a privileged interaction state between hippocampus and cortex by silencing the output of subcortical centres involved in sensory processing or potentially mediating procedural learning. Such a mechanism would cause minimal interference, enabling consolidation of hippocampus-dependent memory.

Web DOI [BibTex]

Web DOI [BibTex]


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Thermodynamic limits of dynamic cooling

Allahverdyan, A., Hovhannisyan, K., Janzing, D., Mahler, G.

Physical Review E, 84(4):16, October 2012 (article)

Abstract
We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature Tmin>0 reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir and over the reservoir energy spectrum. The minimal work needed to reach Tmin grows as 1/Tmin. This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above Tmin. Our results on Tmin>0 prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. We also study cooling via a reservoir consisting of N≫1 identical spins. Here we show that Tmin∝1/N and find the maximal cooling compatible with the minimal work determined by the free energy. Finally we discuss cooling by reservoir with an initially microcanonic state and show that although a purely microcanonic state can yield the zero temperature, the unattainability is recovered when taking into account imperfections in preparing the microcanonic state.

Web DOI [BibTex]

Web DOI [BibTex]


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GLIDE: GPU-Based Linear Regression for Detection of Epistasis

Kam-Thong, T., Azencott, C., Cayton, L., Pütz, B., Altmann, A., Karbalai, N., Sämann, P., Schölkopf, B., Müller-Myhsok, B., Borgwardt, K.

Human Heredity, 73(4):220-236, September 2012 (article)

Abstract
Due to recent advances in genotyping technologies, mapping phenotypes to single loci in the genome has become a standard technique in statistical genetics. However, one-locus mapping fails to explain much of the phenotypic variance in complex traits. Here, we present GLIDE, which maps phenotypes to pairs of genetic loci and systematically searches for the epistatic interactions expected to reveal part of this missing heritability. GLIDE makes use of the computational power of consumer-grade graphics cards to detect such interactions via linear regression. This enabled us to conduct a systematic two-locus mapping study on seven disease data sets from the Wellcome Trust Case Control Consortium and on in-house hippocampal volume data in 6 h per data set, while current single CPU-based approaches require more than a year’s time to complete the same task.

Web [BibTex]

Web [BibTex]


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Fast projection onto mixed-norm balls with applications

Sra, S.

Minining and Knowledge Discovery (DMKD), 25(2):358-377, September 2012 (article)

DOI [BibTex]

DOI [BibTex]


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Bayesian estimation of free energies from equilibrium simulations

Habeck, M.

Physical Review Letters, 109(10):5, September 2012 (article)

Abstract
Free energy calculations are an important tool in statistical physics and biomolecular simulation. This Letter outlines a Bayesian method to estimate free energies from equilibrium Monte Carlo simulations. A Gibbs sampler is developed that allows efficient sampling of free energies and the density of states. The Gibbs sampling output can be used to estimate expected free energy differences and their uncertainties. The probabilistic formulation offers a unifying framework for existing methods such as the weighted histogram analysis method and the multistate Bennett acceptance ratio; both are shown to be approximate versions of the full probabilistic treatment.

Web DOI [BibTex]

Web DOI [BibTex]


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PAC-Bayesian Inequalities for Martingales

Seldin, Y., Laviolette, F., Cesa-Bianchi, N., Shawe-Taylor, J., Auer, P.

IEEE Transactions on Information Theory, 58(12):7086-7093, June 2012 (article)

Abstract
We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. We also present a comparison inequality that bounds expectation of a convex function of martingale difference type variables by expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma inequality.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Entropy Search for Information-Efficient Global Optimization

Hennig, P., Schuler, C.

Journal of Machine Learning Research, 13, pages: 1809-1837, -, June 2012 (article)

Abstract
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum. The reason for the absence of probabilistic global optimizers is that the corresponding inference problem is intractable in several ways. This paper develops desiderata for probabilistic optimization algorithms, then presents a concrete algorithm which addresses each of the computational intractabilities with a sequence of approximations and explicitly adresses the decision problem of maximizing information gain from each evaluation.

PDF Web Project Page [BibTex]

PDF Web Project Page [BibTex]


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A Neuromorphic Architecture for Object Recognition and Motion Anticipation Using Burst-STDP

Nere, A., Olcese, U., Balduzzi, D., Tononi, G.

PLoS ONE, 7(5):17, May 2012 (article)

Abstract
In this work we investigate the possibilities offered by a minimal framework of artificial spiking neurons to be deployed in silico. Here we introduce a hierarchical network architecture of spiking neurons which learns to recognize moving objects in a visual environment and determine the correct motor output for each object. These tasks are learned through both supervised and unsupervised spike timing dependent plasticity (STDP). STDP is responsible for the strengthening (or weakening) of synapses in relation to pre- and post-synaptic spike times and has been described as a Hebbian paradigm taking place both in vitro and in vivo. We utilize a variation of STDP learning, called burst-STDP, which is based on the notion that, since spikes are expensive in terms of energy consumption, then strong bursting activity carries more information than single (sparse) spikes. Furthermore, this learning algorithm takes advantage of homeostatic renormalization, which has been hypothesized to promote memory consolidation during NREM sleep. Using this learning rule, we design a spiking neural network architecture capable of object recognition, motion detection, attention towards important objects, and motor control outputs. We demonstrate the abilities of our design in a simple environment with distractor objects, multiple objects moving concurrently, and in the presence of noise. Most importantly, we show how this neural network is capable of performing these tasks using a simple leaky-integrate-and-fire (LIF) neuron model with binary synapses, making it fully compatible with state-of-the-art digital neuromorphic hardware designs. As such, the building blocks and learning rules presented in this paper appear promising for scalable fully neuromorphic systems to be implemented in hardware chips.

PDF Web DOI [BibTex]


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Online Kernel-based Learning for Task-Space Tracking Robot Control

Nguyen-Tuong, D., Peters, J.

IEEE Transactions on Neural Networks and Learning Systems, 23(9):1417-1425, May 2012 (article)

Abstract
Abstract—Task-space control of redundant robot systems based on analytical models is known to be susceptive to modeling errors. Here, data driven model learning methods may present an interesting alternative approach. However, learning models for task-space tracking control from sampled data is an illposed problem. In particular, the same input data point can yield many different output values, which can form a non-convex solution space. Because the problem is ill-posed, models cannot be learned from such data using common regression methods. While learning of task-space control mappings is globally illposed, it has been shown in recent work that it is locally a well-defined problem. In this paper, we use this insight to formulate a local, kernel-based learning approach for online model learning for task-space tracking control. We propose a parametrization for the local model which makes an application in task-space tracking control of redundant robots possible. The model parametrization further allows us to apply the kerneltrick and, therefore, enables a formulation within the kernel learning framework. For evaluations, we show the ability of the method for online model learning for task-space tracking control of redundant robots.

PDF DOI [BibTex]

PDF DOI [BibTex]


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Information-geometric approach to inferring causal directions

Janzing, D., Mooij, J., Zhang, K., Lemeire, J., Zscheischler, J., Daniušis, P., Steudel, B., Schölkopf, B.

Artificial Intelligence, 182-183, pages: 1-31, May 2012 (article)

Abstract
While conventional approaches to causal inference are mainly based on conditional (in)dependences, recent methods also account for the shape of (conditional) distributions. The idea is that the causal hypothesis “X causes Y” imposes that the marginal distribution PX and the conditional distribution PY|X represent independent mechanisms of nature. Recently it has been postulated that the shortest description of the joint distribution PX,Y should therefore be given by separate descriptions of PX and PY|X. Since description length in the sense of Kolmogorov complexity is uncomputable, practical implementations rely on other notions of independence. Here we define independence via orthogonality in information space. This way, we can explicitly describe the kind of dependence that occurs between PY and PX|Y making the causal hypothesis “Y causes X” implausible. Remarkably, this asymmetry between cause and effect becomes particularly simple if X and Y are deterministically related. We present an inference method that works in this case. We also discuss some theoretical results for the non-deterministic case although it is not clear how to employ them for a more general inference method.

Web DOI [BibTex]

Web DOI [BibTex]


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Sparse regularized regression identifies behaviorally-relevant stimulus features from psychophysical data

Schönfelder, V., Wichmann, F.

Journal of the Acoustical Society of America, 131(5):3953-3969, May 2012 (article)

Abstract
As a prerequisite to quantitative psychophysical models of sensory processing it is necessary to learn to what extent decisions in behavioral tasks depend on specific stimulus features, the perceptual cues. Based on relative linear combination weights, this study demonstrates how stimulus-response data can be analyzed in this regard relying on an L1-regularized multiple logistic regression, a modern statistical procedure developed in machine learning. This method prevents complex models from over-fitting to noisy data. In addition, it enforces “sparse” solutions, a computational approximation to the postulate that a good model should contain the minimal set of predictors necessary to explain the data. In simulations, behavioral data from a classical auditory tone-in-noise detection task were generated. The proposed method is shown to precisely identify observer cues from a large set of covarying, interdependent stimulus features—a setting where standard correlational and regression methods fail. The proposed method succeeds for a wide range of signal-to-noise ratios and for deterministic as well as probabilistic observers. Furthermore, the detailed decision rules of the simulated observers were reconstructed from the estimated linear model weights allowing predictions of responses on the basis of individual stimuli.

Web DOI [BibTex]

Web DOI [BibTex]


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glm-ie: The Generalised Linear Models Inference and Estimation Toolbox

Nickisch, H.

Journal of Machine Learning Research, 13, pages: 1699-1703, May 2012 (article)

Abstract
The glm-ie toolbox contains scalable estimation routines for GLMs (generalised linear models) and SLMs (sparse linear models) as well as an implementation of a scalable convex variational Bayesian inference relaxation. We designed the glm-ie package to be simple, generic and easily expansible. Most of the code is written in Matlab including some The code is fully compatible to both Matlab 7.x and GNU Octave 3.3.x. Abstract Probabilistic classification, sparse linear modelling and logistic regression are covered in a common algorithmical framework.

PDF PDF [BibTex]

PDF PDF [BibTex]


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Feature Selection via Dependence Maximization

Song, L., Smola, A., Gretton, A., Bedo, J., Borgwardt, K.

Journal of Machine Learning Research, 13, pages: 1393-1434, May 2012 (article)

Abstract
We introduce a framework of feature selection based on dependence maximization between the selected features and the labels of an estimation problem, using the Hilbert-Schmidt Independence Criterion. The key idea is that good features should be highly dependent on the labels. Our approach leads to a greedy procedure for feature selection. We show that a number of existing feature selectors are special cases of this framework. Experiments on both artificial and real-world data show that our feature selector works well in practice.

PDF [BibTex]

PDF [BibTex]