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2018


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Maschinelles Lernen: Entwicklung ohne Grenzen?

Schökopf, B.

In Mit Optimismus in die Zukunft schauen. Künstliche Intelligenz - Chancen und Rahmenbedingungen, pages: 26-34, (Editors: Bender, G. and Herbrich, R. and Siebenhaar, K.), B&S Siebenhaar Verlag, 2018 (incollection)

[BibTex]

2018

[BibTex]


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Methods in Psychophysics

Wichmann, F. A., Jäkel, F.

In Stevens’ Handbook of Experimental Psychology and Cognitive Neuroscience, 5 (Methodology), 7, 4th, John Wiley & Sons, Inc., 2018 (inbook)

[BibTex]

[BibTex]


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Transfer Learning for BCIs

Jayaram, V., Fiebig, K., Peters, J., Grosse-Wentrup, M.

In Brain–Computer Interfaces Handbook, pages: 425-442, 22, (Editors: Chang S. Nam, Anton Nijholt and Fabien Lotte), CRC Press, 2018 (incollection)

Project Page [BibTex]

Project Page [BibTex]

2012


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High Gamma-Power Predicts Performance in Brain-Computer Interfacing

Grosse-Wentrup, M., Schölkopf, B.

(3), Max-Planck-Institut für Intelligente Systeme, Tübingen, February 2012 (techreport)

Abstract
Subjects operating a brain-computer interface (BCI) based on sensorimotor rhythms exhibit large variations in performance over the course of an experimental session. Here, we show that high-frequency gamma-oscillations, originating in fronto-parietal networks, predict such variations on a trial-to-trial basis. We interpret this nding as empirical support for an in uence of attentional networks on BCI-performance via modulation of the sensorimotor rhythm.

PDF [BibTex]

2012

PDF [BibTex]


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Expectation-Maximization methods for solving (PO)MDPs and optimal control problems

Toussaint, M., Storkey, A., Harmeling, S.

In Inference and Learning in Dynamic Models, (Editors: Barber, D., Cemgil, A.T. and Chiappa, S.), Cambridge University Press, Cambridge, UK, January 2012 (inbook) In press

PDF [BibTex]

PDF [BibTex]


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Active Learning Methods in Classification of Remote Sensing Images

Bruzzone, L., Persello, C., Demir, B.

In Signal and Image Processing for Remote Sensing, (Editors: CH Chen), CRC Press, Boca Raton, FL, USA, January 2012 (inbook) In press

[BibTex]

[BibTex]


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Inferential structure determination from NMR data

Habeck, M.

In Bayesian methods in structural bioinformatics, pages: 287-312, (Editors: Hamelryck, T., Mardia, K. V. and Ferkinghoff-Borg, J.), Springer, New York, 2012 (inbook)

[BibTex]

[BibTex]


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Robot Learning

Sigaud, O., Peters, J.

In Encyclopedia of the sciences of learning, (Editors: Seel, N.M.), Springer, Berlin, Germany, 2012 (inbook)

Web [BibTex]

Web [BibTex]


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Reinforcement Learning in Robotics: A Survey

Kober, J., Peters, J.

In Reinforcement Learning, 12, pages: 579-610, (Editors: Wiering, M. and Otterlo, M.), Springer, Berlin, Germany, 2012 (inbook)

Abstract
As most action generation problems of autonomous robots can be phrased in terms of sequential decision problems, robotics offers a tremendously important and interesting application platform for reinforcement learning. Similarly, the real-world challenges of this domain pose a major real-world check for reinforcement learning. Hence, the interplay between both disciplines can be seen as promising as the one between physics and mathematics. Nevertheless, only a fraction of the scientists working on reinforcement learning are sufficiently tied to robotics to oversee most problems encountered in this context. Thus, we will bring the most important challenges faced by robot reinforcement learning to their attention. To achieve this goal, we will attempt to survey most work that has successfully applied reinforcement learning to behavior generation for real robots. We discuss how the presented successful approaches have been made tractable despite the complexity of the domain and will study how representations or the inclusion of prior knowledge can make a significant difference. As a result, a particular focus of our chapter lies on the choice between model-based and model-free as well as between value function-based and policy search methods. As a result, we obtain a fairly complete survey of robot reinforcement learning which should allow a general reinforcement learning researcher to understand this domain.

Web DOI [BibTex]

Web DOI [BibTex]


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Higher-Order Tensors in Diffusion MRI

Schultz, T., Fuster, A., Ghosh, A., Deriche, R., Florack, L., Lim, L.

In Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, (Editors: Westin, C. F., Vilanova, A. and Burgeth, B.), Springer, 2012 (inbook) Accepted

[BibTex]

[BibTex]

2011


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Projected Newton-type methods in machine learning

Schmidt, M., Kim, D., Sra, S.

In Optimization for Machine Learning, pages: 305-330, (Editors: Sra, S., Nowozin, S. and Wright, S. J.), MIT Press, Cambridge, MA, USA, December 2011 (inbook)

Abstract
We consider projected Newton-type methods for solving large-scale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newton-type methods by reviewing a canonical projected (quasi-)Newton method. This method, while conceptually pleasing, has a high computation cost per iteration. Thus, we discuss two variants that are more scalable, namely, two-metric projection and inexact projection methods. Finally, we show how to apply the Newton-type framework to handle non-smooth objectives. Examples are provided throughout the chapter to illustrate machine learning applications of our framework.

PDF Web [BibTex]

2011

PDF Web [BibTex]


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Statistical Learning Theory: Models, Concepts, and Results

von Luxburg, U., Schölkopf, B.

In Handbook of the History of Logic, Vol. 10: Inductive Logic, 10, pages: 651-706, (Editors: Gabbay, D. M., Hartmann, S. and Woods, J. H.), Elsevier North Holland, Amsterdam, Netherlands, May 2011 (inbook)

Abstract
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms and is arguably one of the most beautifully developed branches of artificial intelligence in general. It originated in Russia in the 1960s and gained wide popularity in the 1990s following the development of the so-called Support Vector Machine (SVM), which has become a standard tool for pattern recognition in a variety of domains ranging from computer vision to computational biology. Providing the basis of new learning algorithms, however, was not the only motivation for developing statistical learning theory. It was just as much a philosophical one, attempting to answer the question of what it is that allows us to draw valid conclusions from empirical data. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We do not assume that the reader has a deep background in mathematics, statistics, or computer science. Given the nature of the subject matter, however, some familiarity with mathematical concepts and notations and some intuitive understanding of basic probability is required. There exist many excellent references to more technical surveys of the mathematics of statistical learning theory: the monographs by one of the founders of statistical learning theory ([Vapnik, 1995], [Vapnik, 1998]), a brief overview over statistical learning theory in Section 5 of [Sch{\"o}lkopf and Smola, 2002], more technical overview papers such as [Bousquet et al., 2003], [Mendelson, 2003], [Boucheron et al., 2005], [Herbrich and Williamson, 2002], and the monograph [Devroye et al., 1996].

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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PAC-Bayesian Analysis of Martingales and Multiarmed Bandits

Seldin, Y., Laviolette, F., Shawe-Taylor, J., Peters, J., Auer, P.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2011 (techreport)

Abstract
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This lemma provides an alternative tool to Hoeffding-Azuma inequality to bound concentration of martingale values. Our second approach is based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis. We also introduce a way to apply PAC-Bayesian analysis in situation of limited feedback. We combine the new tools to derive PAC-Bayesian generalization and regret bounds for the multiarmed bandit problem. Although our regret bound is not yet as tight as state-of-the-art regret bounds based on other well-established techniques, our results significantly expand the range of potential applications of PAC-Bayesian analysis and introduce a new analysis tool to reinforcement learning and many other fields, where martingales and limited feedback are encountered.

PDF Web [BibTex]

PDF Web [BibTex]


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Non-stationary Correction of Optical Aberrations

Schuler, C., Hirsch, M., Harmeling, S., Schölkopf, B.

(1), Max Planck Institute for Intelligent Systems, Tübingen, Germany, May 2011 (techreport)

Abstract
Taking a sharp photo at several megapixel resolution traditionally relies on high grade lenses. In this paper, we present an approach to alleviate image degradations caused by imperfect optics. We rely on a calibration step to encode the optical aberrations in a space-variant point spread function and obtain a corrected image by non-stationary deconvolution. By including the Bayer array in our image formation model, we can perform demosaicing as part of the deconvolution.

PDF [BibTex]

PDF [BibTex]


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Multiple Kernel Learning: A Unifying Probabilistic Viewpoint

Nickisch, H., Seeger, M.

Max Planck Institute for Biological Cybernetics, March 2011 (techreport)

Abstract
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the marginal likelihood and contains many regularised risk approaches as special cases. Furthermore, we derive an efficient and provably convergent optimisation algorithm.

Web [BibTex]

Web [BibTex]


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Multiple testing, uncertainty and realistic pictures

Langovoy, M., Wittich, O.

(2011-004), EURANDOM, Technische Universiteit Eindhoven, January 2011 (techreport)

Abstract
We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise distributions. We achieve this by proving an uncertainty principle for percolation on nite lattices.

PDF [BibTex]

PDF [BibTex]


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Robot Learning

Peters, J., Tedrake, R., Roy, N., Morimoto, J.

In Encyclopedia of Machine Learning, pages: 865-869, Encyclopedia of machine learning, (Editors: Sammut, C. and Webb, G. I.), Springer, New York, NY, USA, January 2011 (inbook)

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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What You Expect Is What You Get? Potential Use of Contingent Negative Variation for Passive BCI Systems in Gaze-Based HCI

Ihme, K., Zander, TO.

In Affective Computing and Intelligent Interaction, 6975, pages: 447-456, Lecture Notes in Computer Science, (Editors: D’Mello, S., Graesser, A., Schuller, B. and Martin, J.-C.), Springer, Berlin, Germany, 2011 (inbook)

Abstract
When using eye movements for cursor control in human-computer interaction (HCI), it may be difficult to find an appropriate substitute for the click operation. Most approaches make use of dwell times. However, in this context the so-called Midas-Touch-Problem occurs which means that the system wrongly interprets fixations due to long processing times or spontaneous dwellings of the user as command. Lately it has been shown that brain-computer interface (BCI) input bears good prospects to overcome this problem using imagined hand movements to elicit a selection. The current approach tries to develop this idea further by exploring potential signals for the use in a passive BCI, which would have the advantage that the brain signals used as input are generated automatically without conscious effort of the user. To explore event-related potentials (ERPs) giving information about the user’s intention to select an object, 32-channel electroencephalography (EEG) was recorded from ten participants interacting with a dwell-time-based system. Comparing ERP signals during the dwell time with those occurring during fixations on a neutral cross hair, a sustained negative slow cortical potential at central electrode sites was revealed. This negativity might be a contingent negative variation (CNV) reflecting the participants’ anticipation of the upcoming selection. Offline classification suggests that the CNV is detectable in single trial (mean accuracy 74.9 %). In future, research on the CNV should be accomplished to ensure its stable occurence in human-computer interaction and render possible its use as a potential substitue for the click operation.

DOI [BibTex]

DOI [BibTex]


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Kernel Methods in Bioinformatics

Borgwardt, KM.

In Handbook of Statistical Bioinformatics, pages: 317-334, Springer Handbooks of Computational Statistics ; 3, (Editors: Lu, H.H.-S., Schölkopf, B. and Zhao, H.), Springer, Berlin, Germany, 2011 (inbook)

Abstract
Kernel methods have now witnessed more than a decade of increasing popularity in the bioinformatics community. In this article, we will compactly review this development, examining the areas in which kernel methods have contributed to computational biology and describing the reasons for their success.

PDF DOI [BibTex]

PDF DOI [BibTex]


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Cue Combination: Beyond Optimality

Rosas, P., Wichmann, F.

In Sensory Cue Integration, pages: 144-152, (Editors: Trommershäuser, J., Körding, K. and Landy, M. S.), Oxford University Press, 2011 (inbook)

[BibTex]

[BibTex]


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Nonconvex proximal splitting: batch and incremental algorithms

Sra, S.

(2), Max Planck Institute for Intelligent Systems, Tübingen, Germany, 2011 (techreport)

Abstract
Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems having composite objectives (this includes the extensively studied convex, composite objective problems as a special case). For this subclass, we introduce a powerful, new framework that permits asymptotically non-vanishing perturbations. In particular, we develop perturbation-based batch and incremental (online like) nonconvex proximal splitting algorithms. To our knowledge, this is the rst time that such perturbation-based nonconvex splitting algorithms are being proposed and analyzed. While the main contribution of the paper is the theoretical framework, we complement our results by presenting some empirical results on matrix factorization.

PDF [BibTex]

PDF [BibTex]

2008


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Frequent Subgraph Retrieval in Geometric Graph Databases

Nowozin, S., Tsuda, K.

(180), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2008 (techreport)

Abstract
Discovery of knowledge from geometric graph databases is of particular importance in chemistry and biology, because chemical compounds and proteins are represented as graphs with 3D geometric coordinates. In such applications, scientists are not interested in the statistics of the whole database. Instead they need information about a novel drug candidate or protein at hand, represented as a query graph. We propose a polynomial-delay algorithm for geometric frequent subgraph retrieval. It enumerates all subgraphs of a single given query graph which are frequent geometric epsilon-subgraphs under the entire class of rigid geometric transformations in a database. By using geometric epsilon-subgraphs, we achieve tolerance against variations in geometry. We compare the proposed algorithm to gSpan on chemical compound data, and we show that for a given minimum support the total number of frequent patterns is substantially limited by requiring geometric matching. Although the computation time per pattern is larger than for non-geometric graph mining, the total time is within a reasonable level even for small minimum support.

PDF [BibTex]

2008

PDF [BibTex]


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Simultaneous Implicit Surface Reconstruction and Meshing

Giesen, J., Maier, M., Schölkopf, B.

(179), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2008 (techreport)

Abstract
We investigate an implicit method to compute a piecewise linear representation of a surface from a set of sample points. As implicit surface functions we use the weighted sum of piecewise linear kernel functions. For such a function we can partition Rd in such a way that these functions are linear on the subsets of the partition. For each subset in the partition we can then compute the zero level set of the function exactly as the intersection of a hyperplane with the subset.

PDF [BibTex]

PDF [BibTex]


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Taxonomy Inference Using Kernel Dependence Measures

Blaschko, M., Gretton, A.

(181), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2008 (techreport)

Abstract
We introduce a family of unsupervised algorithms, numerical taxonomy clustering, to simultaneously cluster data, and to learn a taxonomy that encodes the relationship between the clusters. The algorithms work by maximizing the dependence between the taxonomy and the original data. The resulting taxonomy is a more informative visualization of complex data than simple clustering; in addition, taking into account the relations between different clusters is shown to substantially improve the quality of the clustering, when compared with state-of-the-art algorithms in the literature (both spectral clustering and a previous dependence maximization approach). We demonstrate our algorithm on image and text data.

PDF [BibTex]

PDF [BibTex]


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Infinite Kernel Learning

Gehler, P., Nowozin, S.

(178), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, October 2008 (techreport)

Abstract
In this paper we consider the problem of automatically learning the kernel from general kernel classes. Specifically we build upon the Multiple Kernel Learning (MKL) framework and in particular on the work of (Argyriou, Hauser, Micchelli, & Pontil, 2006). We will formulate a Semi-Infinite Program (SIP) to solve the problem and devise a new algorithm to solve it (Infinite Kernel Learning, IKL). The IKL algorithm is applicable to both the finite and infinite case and we find it to be faster and more stable than SimpleMKL (Rakotomamonjy, Bach, Canu, & Grandvalet, 2007) for cases of many kernels. In the second part we present the first large scale comparison of SVMs to MKL on a variety of benchmark datasets, also comparing IKL. The results show two things: a) for many datasets there is no benefit in linearly combining kernels with MKL/IKL instead of the SVM classifier, thus the flexibility of using more than one kernel seems to be of no use, b) on some datasets IKL yields impressive increases in accuracy over SVM/MKL due to the possibility of using a largely increased kernel set. In those cases, IKL remains practical, whereas both cross-validation or standard MKL is infeasible.

PDF Web [BibTex]

PDF Web [BibTex]


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Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models

Seeger, M., Nickisch, H.

(175), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2008 (techreport)

PDF [BibTex]

PDF [BibTex]


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Block-Iterative Algorithms for Non-Negative Matrix Approximation

Sra, S.

(176), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2008 (techreport)

Abstract
In this report we present new algorithms for non-negative matrix approximation (NMA), commonly known as the NMF problem. Our methods improve upon the well-known methods of Lee & Seung [19] for both the Frobenius norm as well the Kullback-Leibler divergence versions of the problem. For the latter problem, our results are especially interesting because it seems to have witnessed much lesser algorithmic progress as compared to the Frobenius norm NMA problem. Our algorithms are based on a particular block-iterative acceleration technique for EM, which preserves the multiplicative nature of the updates and also ensures monotonicity. Furthermore, our algorithms also naturally apply to the Bregman-divergence NMA algorithms of Dhillon and Sra [8]. Experimentally, we show that our algorithms outperform the traditional Lee/Seung approach most of the time.

PDF [BibTex]

PDF [BibTex]


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Approximation Algorithms for Bregman Clustering Co-clustering and Tensor Clustering

Sra, S., Jegelka, S., Banerjee, A.

(177), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2008 (techreport)

Abstract
The Euclidean K-means problem is fundamental to clustering and over the years it has been intensely investigated. More recently, generalizations such as Bregman k-means [8], co-clustering [10], and tensor (multi-way) clustering [40] have also gained prominence. A well-known computational difficulty encountered by these clustering problems is the NP-Hardness of the associated optimization task, and commonly used methods guarantee at most local optimality. Consequently, approximation algorithms of varying degrees of sophistication have been developed, though largely for the basic Euclidean K-means (or `1-norm K-median) problem. In this paper we present approximation algorithms for several Bregman clustering problems by building upon the recent paper of Arthur and Vassilvitskii [5]. Our algorithms obtain objective values within a factor O(logK) for Bregman k-means, Bregman co-clustering, Bregman tensor clustering, and weighted kernel k-means. To our knowledge, except for some special cases, approximation algorithms have not been considered for these general clustering problems. There are several important implications of our work: (i) under the same assumptions as Ackermann et al. [1] it yields a much faster algorithm (non-exponential in K, unlike [1]) for information-theoretic clustering, (ii) it answers several open problems posed by [4], including generalizations to Bregman co-clustering, and tensor clustering, (iii) it provides practical and easy to implement methods—in contrast to several other common approximation approaches.

PDF [BibTex]

PDF [BibTex]


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Combining Appearance and Motion for Human Action Classification in Videos

Dhillon, P., Nowozin, S., Lampert, C.

(174), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, August 2008 (techreport)

Abstract
We study the question of activity classification in videos and present a novel approach for recognizing human action categories in videos by combining information from appearance and motion of human body parts. Our approach uses a tracking step which involves Particle Filtering and a local non - parametric clustering step. The motion information is provided by the trajectory of the cluster modes of a local set of particles. The statistical information about the particles of that cluster over a number of frames provides the appearance information. Later we use a “Bag ofWords” model to build one histogram per video sequence from the set of these robust appearance and motion descriptors. These histograms provide us characteristic information which helps us to discriminate among various human actions and thus classify them correctly. We tested our approach on the standard KTH and Weizmann human action datasets and the results were comparable to the state of the art. Additionally our approach is able to distinguish between activities that involve the motion of complete body from those in which only certain body parts move. In other words, our method discriminates well between activities with “gross motion” like running, jogging etc. and “local motion” like waving, boxing etc.

PDF [BibTex]

PDF [BibTex]


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Example-based Learning for Single-image Super-resolution and JPEG Artifact Removal

Kim, K., Kwon, Y.

(173), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, August 2008 (techreport)

Abstract
This paper proposes a framework for single-image super-resolution and JPEG artifact removal. The underlying idea is to learn a map from input low-quality images (suitably preprocessed low-resolution or JPEG encoded images) to target high-quality images based on example pairs of input and output images. To retain the complexity of the resulting learning problem at a moderate level, a patch-based approach is taken such that kernel ridge regression (KRR) scans the input image with a small window (patch) and produces a patchvalued output for each output pixel location. These constitute a set of candidate images each of which reflects different local information. An image output is then obtained as a convex combination of candidates for each pixel based on estimated confidences of candidates. To reduce the time complexity of training and testing for KRR, a sparse solution is found by combining the ideas of kernel matching pursuit and gradient descent. As a regularized solution, KRR leads to a better generalization than simply storing the examples as it has been done in existing example-based super-resolution algorithms and results in much less noisy images. However, this may introduce blurring and ringing artifacts around major edges as sharp changes are penalized severely. A prior model of a generic image class which takes into account the discontinuity property of images is adopted to resolve this problem. Comparison with existing super-resolution and JPEG artifact removal methods shows the effectiveness of the proposed method. Furthermore, the proposed method is generic in that it has the potential to be applied to many other image enhancement applications.

PDF [BibTex]

PDF [BibTex]


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Unsupervised Bayesian Time-series Segmentation based on Linear Gaussian State-space Models

Chiappa, S.

(171), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, June 2008 (techreport)

Abstract
Unsupervised time-series segmentation in the general scenario in which the number of segment-types and segment boundaries are a priori unknown is a fundamental problem in many applications and requires an accurate segmentation model as well as a way of determining an appropriate number of segment-types. In most approaches, segmentation and determination of number of segment-types are addressed in two separate steps, since the segmentation model assumes a predefined number of segment-types. The determination of number of segment-types is thus achieved by training and comparing several separate models. In this paper, we take a Bayesian approach to a segmentation model based on linear Gaussian state-space models to achieve structure selection within the model. An appropriate prior distribution on the parameters is used to enforce a sparse parametrization, such that the model automatically selects the smallest number of underlying dynamical systems that explain the data well and a parsimonious structure for each dynamical system. As the resulting model is computationally intractable, we introduce a variational approximation, in which a reformulation of the problem enables to use an efficient inference algorithm.

[BibTex]

[BibTex]


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A New Non-monotonic Gradient Projection Method for the Non-negative Least Squares Problem

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

(TR-08-28), University of Texas, Austin, TX, USA, June 2008 (techreport)

Web [BibTex]

Web [BibTex]


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Non-monotonic Poisson Likelihood Maximization

Sra, S., Kim, D., Schölkopf, B.

(170), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2008 (techreport)

Abstract
This report summarizes the theory and some main applications of a new non-monotonic algorithm for maximizing a Poisson Likelihood, which for Positron Emission Tomography (PET) is equivalent to minimizing the associated Kullback-Leibler Divergence, and for Transmission Tomography is similar to maximizing the dual of a maximum entropy problem. We call our method non-monotonic maximum likelihood (NMML) and show its application to different problems such as tomography and image restoration. We discuss some theoretical properties such as convergence for our algorithm. Our experimental results indicate that speedups obtained via our non-monotonic methods are substantial.

PDF [BibTex]

PDF [BibTex]


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New Frontiers in Characterizing Structure and Dynamics by NMR

Nilges, M., Markwick, P., Malliavin, TE., Rieping, W., Habeck, M.

In Computational Structural Biology: Methods and Applications, pages: 655-680, (Editors: Schwede, T. , M. C. Peitsch), World Scientific, New Jersey, NJ, USA, May 2008 (inbook)

Abstract
Nuclear Magnetic Resonance (NMR) spectroscopy has emerged as the method of choice for studying both the structure and the dynamics of biological macromolecule in solution. Despite the maturity of the NMR method for structure determination, its application faces a number of challenges. The method is limited to systems of relatively small molecular mass, data collection times are long, data analysis remains a lengthy procedure, and it is difficult to evaluate the quality of the final structures. The last years have seen significant advances in experimental techniques to overcome or reduce some limitations. The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time–scales from picoseconds to seconds. NMR is unique in its ability to obtain dynamic information on an atomic scale. The experimental information on structure and dynamics is intricately mixed. It is however difficult to unite both structural and dynamical information into one consistent model, and protocols for the determination of structure and dynamics are performed independently. This chapter deals with the challenges posed by the interpretation of NMR data on structure and dynamics. We will first relate the standard structure calculation methods to Bayesian probability theory. We will then briefly describe the advantages of a fully Bayesian treatment of structure calculation. Then, we will illustrate the advantages of using Bayesian reasoning at least partly in standard structure calculations. The final part will be devoted to interpretation of experimental data on dynamics.

Web [BibTex]

Web [BibTex]


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A Kernel Method for the Two-sample Problem

Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., Smola, A.

(157), Max-Planck-Institute for Biological Cybernetics Tübingen, April 2008 (techreport)

Abstract
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg.~a Banach space). We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.

PDF [BibTex]

PDF [BibTex]


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Energy Functionals for Manifold-valued Mappings and Their Properties

Hein, M., Steinke, F., Schölkopf, B.

(167), Max Planck Institute for Biological Cybernetics, Tübingen, January 2008 (techreport)

Abstract
This technical report is merely an extended version of the appendix of Steinke et.al. "Manifold-valued Thin-Plate Splines with Applications in Computer Graphics" (2008) with complete proofs, which had to be omitted due to space restrictions. This technical report requires a basic knowledge of differential geometry. However, apart from that requirement the technical report is self-contained.

PDF [BibTex]

PDF [BibTex]


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A Robot System for Biomimetic Navigation: From Snapshots to Metric Embeddings of View Graphs

Franz, MO., Stürzl, W., Reichardt, W., Mallot, HA.

In Robotics and Cognitive Approaches to Spatial Mapping, pages: 297-314, Springer Tracts in Advanced Robotics ; 38, (Editors: Jefferies, M.E. , W.-K. Yeap), Springer, Berlin, Germany, 2008 (inbook)

Abstract
Complex navigation behaviour (way-finding) involves recognizing several places and encoding a spatial relationship between them. Way-finding skills can be classified into a hierarchy according to the complexity of the tasks that can be performed [8]. The most basic form of way-finding is route navigation, followed by topological navigation where several routes are integrated into a graph-like representation. The highest level, survey navigation, is reached when this graph can be embedded into a common reference frame. In this chapter, we present the building blocks for a biomimetic robot navigation system that encompasses all levels of this hierarchy. As a local navigation method, we use scene-based homing. In this scheme, a goal location is characterized either by a panoramic snapshot of the light intensities as seen from the place, or by a record of the distances to the surrounding objects. The goal is found by moving in the direction that minimizes the discrepancy between the recorded intensities or distances and the current sensory input. For learning routes, the robot selects distinct views during exploration that are close enough to be reached by snapshot-based homing. When it encounters already visited places during route learning, it connects the routes and thus forms a topological representation of its environment termed a view graph. The final stage, survey navigation, is achieved by a graph embedding procedure which complements the topologic information of the view graph with odometric position estimates. Calculation of the graph embedding is done with a modified multidimensional scaling algorithm which makes use of distances and angles between nodes.

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]

2006


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A New Projected Quasi-Newton Approach for the Nonnegative Least Squares Problem

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

(TR-06-54), Univ. of Texas, Austin, December 2006 (techreport)

PDF [BibTex]

2006

PDF [BibTex]


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Probabilistic inference for solving (PO)MDPs

Toussaint, M., Harmeling, S., Storkey, A.

(934), School of Informatics, University of Edinburgh, December 2006 (techreport)

PDF [BibTex]

PDF [BibTex]


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Minimal Logical Constraint Covering Sets

Sinz, F., Schölkopf, B.

(155), Max Planck Institute for Biological Cybernetics, Tübingen, December 2006 (techreport)

Abstract
We propose a general framework for computing minimal set covers under class of certain logical constraints. The underlying idea is to transform the problem into a mathematical programm under linear constraints. In this sense it can be seen as a natural extension of the vector quantization algorithm proposed by Tipping and Schoelkopf. We show which class of logical constraints can be cast and relaxed into linear constraints and give an algorithm for the transformation.

PDF [BibTex]

PDF [BibTex]


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Prediction of Protein Function from Networks

Shin, H., Tsuda, K.

In Semi-Supervised Learning, pages: 361-376, Adaptive Computation and Machine Learning, (Editors: Chapelle, O. , B. Schölkopf, A. Zien), MIT Press, Cambridge, MA, USA, November 2006 (inbook)

Abstract
In computational biology, it is common to represent domain knowledge using graphs. Frequently there exist multiple graphs for the same set of nodes, representing information from different sources, and no single graph is sufficient to predict class labels of unlabelled nodes reliably. One way to enhance reliability is to integrate multiple graphs, since individual graphs are partly independent and partly complementary to each other for prediction. In this chapter, we describe an algorithm to assign weights to multiple graphs within graph-based semi-supervised learning. Both predicting class labels and searching for weights for combining multiple graphs are formulated into one convex optimization problem. The graph-combining method is applied to functional class prediction of yeast proteins.When compared with individual graphs, the combined graph with optimized weights performs significantly better than any single graph.When compared with the semidefinite programming-based support vector machine (SDP/SVM), it shows comparable accuracy in a remarkably short time. Compared with a combined graph with equal-valued weights, our method could select important graphs without loss of accuracy, which implies the desirable property of integration with selectivity.

Web [BibTex]

Web [BibTex]


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Discrete Regularization

Zhou, D., Schölkopf, B.

In Semi-supervised Learning, pages: 237-250, Adaptive computation and machine learning, (Editors: O Chapelle and B Schölkopf and A Zien), MIT Press, Cambridge, MA, USA, November 2006 (inbook)

Abstract
Many real-world machine learning problems are situated on finite discrete sets, including dimensionality reduction, clustering, and transductive inference. A variety of approaches for learning from finite sets has been proposed from different motivations and for different problems. In most of those approaches, a finite set is modeled as a graph, in which the edges encode pairwise relationships among the objects in the set. Consequently many concepts and methods from graph theory are adopted. In particular, the graph Laplacian is widely used. In this chapter we present a systemic framework for learning from a finite set represented as a graph. We develop discrete analogues of a number of differential operators, and then construct a discrete analogue of classical regularization theory based on those discrete differential operators. The graph Laplacian based approaches are special cases of this general discrete regularization framework. An important thing implied in this framework is that we have a wide choices of regularization on graph in addition to the widely-used graph Laplacian based one.

PDF Web [BibTex]

PDF Web [BibTex]


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New Methods for the P300 Visual Speller

Biessmann, F.

(1), (Editors: Hill, J. ), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2006 (techreport)

PDF [BibTex]

PDF [BibTex]


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Geometric Analysis of Hilbert Schmidt Independence criterion based ICA contrast function

Shen, H., Jegelka, S., Gretton, A.

(PA006080), National ICT Australia, Canberra, Australia, October 2006 (techreport)

Web [BibTex]

Web [BibTex]


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A tutorial on spectral clustering

von Luxburg, U.

(149), Max Planck Institute for Biological Cybernetics, Tübingen, August 2006 (techreport)

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. Nevertheless, on the first glance spectral clustering looks a bit mysterious, and it is not obvious to see why it works at all and what it really does. This article is a tutorial introduction to spectral clustering. 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 [BibTex]

PDF [BibTex]


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Towards the Inference of Graphs on Ordered Vertexes

Zien, A., Raetsch, G., Ong, C.

(150), Max Planck Institute for Biological Cybernetics, Tübingen, August 2006 (techreport)

Abstract
We propose novel methods for machine learning of structured output spaces. Specifically, we consider outputs which are graphs with vertices that have a natural order. We consider the usual adjacency matrix representation of graphs, as well as two other representations for such a graph: (a) decomposing the graph into a set of paths, (b) converting the graph into a single sequence of nodes with labeled edges. For each of the three representations, we propose an encoding and decoding scheme. We also propose an evaluation measure for comparing two graphs.

PDF [BibTex]

PDF [BibTex]


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Nonnegative Matrix Approximation: Algorithms and Applications

Sra, S., Dhillon, I.

Univ. of Texas, Austin, May 2006 (techreport)

[BibTex]

[BibTex]


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An Automated Combination of Sequence Motif Kernels for Predicting Protein Subcellular Localization

Zien, A., Ong, C.

(146), Max Planck Institute for Biological Cybernetics, Tübingen, April 2006 (techreport)

Abstract
Protein subcellular localization is a crucial ingredient to many important inferences about cellular processes, including prediction of protein function and protein interactions. While many predictive computational tools have been proposed, they tend to have complicated architectures and require many design decisions from the developer. We propose an elegant and fully automated approach to building a prediction system for protein subcellular localization. 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 further propose a multiclass support vector machine 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 generalize our method to optimize over multiple kernels at the same time. We compare our automated approach to four other predictors on three different datasets.

PDF Web [BibTex]

PDF Web [BibTex]


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Training a Support Vector Machine in the Primal

Chapelle, O.

(147), Max Planck Institute for Biological Cybernetics, Tübingen, April 2006, The version in the "Large Scale Kernel Machines" book is more up to date. (techreport)

Abstract
Most literature on Support Vector Machines (SVMs) concentrate on the dual optimization problem. In this paper, we would like to point out that the primal problem can also be solved efficiently, both for linear and non-linear SVMs, and there is no reason for ignoring it. Moreover, from the primal point of view, new families of algorithms for large scale SVM training can be investigated.

PDF [BibTex]

PDF [BibTex]


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Cross-Validation Optimization for Structured Hessian Kernel Methods

Seeger, M., Chapelle, O.

Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, February 2006 (techreport)

Abstract
We address the problem of learning hyperparameters in kernel methods for which the Hessian of the objective is structured. We propose an approximation to the cross-validation log likelihood whose gradient can be computed analytically, solving the hyperparameter learning problem efficiently through nonlinear optimization. Crucially, our learning method is based entirely on matrix-vector multiplication primitives with the kernel matrices and their derivatives, allowing straightforward specialization to new kernels or to large datasets. When applied to the problem of multi-way classification, our method scales linearly in the number of classes and gives rise to state-of-the-art results on a remote imaging task.

PDF Web [BibTex]

PDF Web [BibTex]