Publications | Empirical Inference - Max Planck Institute for Intelligent Systems

In the series of our earlier papers on the subject, we proposed a novel statistical hy- pothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed algorithms that allowed to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of un- known distribution. No boundary shape constraints were imposed on the objects, only a weak bulk condition for the object's interior was required. Our algorithms have linear complexity and exponential accuracy. In the present paper, we describe an implementation of our nonparametric hypothesis testing method. We provide a program that can be used for statistical experiments in image processing. This program is written in the statistical programming language R.

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2010

Langovoy, M., Wittich, O. Computationally efficient algorithms for statistical image processing: Implementation in R (2010-053), EURANDOM, Technische Universiteit Eindhoven, December 2010 (techreport)

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Fast Convergent Algorithms for Expectation Propagation Approximate Bayesian Inference

Seeger, M., Nickisch, H.

Max Planck Institute for Biological Cybernetics, December 2010 (techreport)

Abstract

We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is provably convergent. By marrying convergent EP ideas from (Opper&Winther 05) with covariance decoupling techniques (Wipf&Nagarajan 08, Nickisch&Seeger 09), it runs at least an order of magnitude faster than the most commonly used EP solver.

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Seeger, M., Nickisch, H. Fast Convergent Algorithms for Expectation Propagation Approximate Bayesian Inference Max Planck Institute for Biological Cybernetics, December 2010 (techreport)

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Comparative Quantitative Evaluation of MR-Based Attenuation Correction Methods in Combined Brain PET/MR

Mantlik, F., Hofmann, M., Bezrukov, I., Kolb, A., Beyer, T., Reimold, M., Pichler, B., Schölkopf, B.

2010(M08-4), 2010 Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC), November 2010 (talk)

Abstract

Combined PET/MR provides at the same time molecular and functional imaging as well as excellent soft tissue contrast. It does not allow one to directly measure the attenuation properties of scanned tissues, despite the fact that accurate attenuation maps are necessary for quantitative PET imaging. Several methods have therefore been proposed for MR-based attenuation correction (MR-AC). So far, they have only been evaluated on data acquired from separate MR and PET scanners. We evaluated several MR-AC methods on data from 10 patients acquired on a combined BrainPET/MR scanner. This allowed the consideration of specific PET/MR issues, such as the RF coil that attenuates and scatters 511 keV gammas. We evaluated simple MR thresholding methods as well as atlas and machine learning-based MR-AC. CT-based AC served as gold standard reference. To comprehensively evaluate the MR-AC accuracy, we used RoIs from 2 anatomic brain atlases with different levels of detail. Visual inspection of the PET images indicated that even the basic FLASH threshold MR-AC may be sufficient for several applications. Using a UTE sequence for bone prediction in MR-based thresholding occasionally led to false prediction of bone tissue inside the brain, causing a significant overestimation of PET activity. Although it yielded a lower mean underestimation of activity, it exhibited the highest variance of all methods. The atlas averaging approach had a smaller mean error, but showed high maximum overestimation on the RoIs of the more detailed atlas. The Nave Bayes and Atlas-Patch MR-AC yielded the smallest variance, and the Atlas-Patch also showed the smallest mean error. In conclusion, Atlas-based AC using only MR information on the BrainPET/MR yields a high level of accuracy that is sufficient for clinical quantitative imaging requirements. The Atlas-Patch approach was superior to alternative atlas-based methods, yielding a quantification error below 10% for all RoIs except very small ones.

[BibTex]

Mantlik, F., Hofmann, M., Bezrukov, I., Kolb, A., Beyer, T., Reimold, M., Pichler, B., Schölkopf, B. Comparative Quantitative Evaluation of MR-Based Attenuation Correction Methods in Combined Brain PET/MR 2010(M08-4), 2010 Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC), November 2010 (talk)

[BibTex]

A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering

Seldin, Y.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2010 (techreport)

Abstract

We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph clustering with other possible ways to model the graph. We adapt the PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009) to derive a PAC-Bayesian generalization bound for graph clustering. The bound shows that graph clustering should optimize a trade-off between empirical data fit and the mutual information that clusters preserve on the graph nodes. A similar trade-off derived from information-theoretic considerations was already shown to produce state-of-the-art results in practice (Slonim et al., 2005; Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by providing a better theoretical foundation, suggesting formal generalization guarantees, and offering a more accurate way to deal with finite sample issues. We derive a bound minimization algorithm and show that it provides good results in real-life problems and that the derived PAC-Bayesian bound is reasonably tight.

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Seldin, Y. A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2010 (techreport)

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Sparse nonnegative matrix approximation: new formulations and algorithms

Tandon, R., Sra, S.

(193), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2010 (techreport)

Abstract

We introduce several new formulations for sparse nonnegative matrix approximation. Subsequently, we solve these formulations by developing generic algorithms. Further, to help selecting a particular sparse formulation, we briefly discuss the interpretation of each formulation. Finally, preliminary experiments are presented to illustrate the behavior of our formulations and algorithms.

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Tandon, R., Sra, S. Sparse nonnegative matrix approximation: new formulations and algorithms (193), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2010 (techreport)

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Robust nonparametric detection of objects in noisy images

Langovoy, M., Wittich, O.

(2010-049), EURANDOM, Technische Universiteit Eindhoven, September 2010 (techreport)

Abstract

We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore im- portant connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a nite sample performance of our test.

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Langovoy, M., Wittich, O. Robust nonparametric detection of objects in noisy images (2010-049), EURANDOM, Technische Universiteit Eindhoven, September 2010 (techreport)

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Statistical image analysis and percolation theory

Davies, P., Langovoy, M., Wittich, O.

73rd Annual Meeting of the Institute of Mathematical Statistics (IMS), August 2010 (talk)

Abstract

We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and can be heavy-tailed. We view the object detection problem as hypothesis testing for discrete statistical inverse problems. We present an algorithm that allows to detect objects of various shapes in noisy images. We prove results on consistency and algorithmic complexity of our procedures.

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Davies, P., Langovoy, M., Wittich, O. Statistical image analysis and percolation theory 73rd Annual Meeting of the Institute of Mathematical Statistics (IMS), August 2010 (talk)

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

Seeger, M., Nickisch, H.

Max Planck Institute for Biological Cybernetics, August 2010 (techreport)

Abstract

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

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Seeger, M., Nickisch, H. Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models Max Planck Institute for Biological Cybernetics, August 2010 (techreport)

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Cooperative Cuts for Image Segmentation

Jegelka, S., Bilmes, J.

(UWEETR-1020-0003), University of Washington, Washington DC, USA, August 2010 (techreport)

Abstract

We propose a novel framework for graph-based cooperative regularization that uses submodular costs on graph edges. We introduce an efficient iterative algorithm to solve the resulting hard discrete optimization problem, and show that it has a guaranteed approximation factor. The edge-submodular formulation is amenable to the same extensions as standard graph cut approaches, and applicable to a range of problems. We apply this method to the image segmentation problem. Specifically, Here, we apply it to introduce a discount for homogeneous boundaries in binary image segmentation on very difficult images, precisely, long thin objects and color and grayscale images with a shading gradient. The experiments show that significant portions of previously truncated objects are now preserved.

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Jegelka, S., Bilmes, J. Cooperative Cuts for Image Segmentation (UWEETR-1020-0003), University of Washington, Washington DC, USA, August 2010 (techreport)

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Statistical image analysis and percolation theory

Langovoy, M., Wittich, O.

28th European Meeting of Statisticians (EMS), August 2010 (talk)

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Langovoy, M., Wittich, O. Statistical image analysis and percolation theory 28th European Meeting of Statisticians (EMS), August 2010 (talk)

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Fast algorithms for total-variationbased optimization

Barbero, A., Sra, S.

(194), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2010 (techreport)

Abstract

We derive a number of methods to solve efficiently simple optimization problems subject to a totalvariation (TV) regularization, under different norms of the TV operator and both for the case of 1-dimensional and 2-dimensional data. In spite of the non-smooth, non-separable nature of the TV terms considered, we show that a dual formulation with strong structure can be derived. Taking advantage of this structure we develop adaptions of existing algorithms from the optimization literature, resulting in efficient methods for the problem at hand. Experimental results show that for 1-dimensional data the proposed methods achieve convergence within good accuracy levels in practically linear time, both for L1 and L2 norms. For the more challenging 2-dimensional case a performance of order O(N2 log2 N) for N x N inputs is achieved when using the L2 norm. A final section suggests possible extensions and lines of further work.

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Barbero, A., Sra, S. Fast algorithms for total-variationbased optimization (194), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2010 (techreport)

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Cooperative Cuts: Graph Cuts with Submodular Edge Weights

Jegelka, S., Bilmes, J.

24th European Conference on Operational Research (EURO XXIV), July 2010 (talk)

Abstract

We introduce cooperative cut, a minimum cut problem whose cost is a submodular function on sets of edges: the cost of an edge that is added to a cut set depends on the edges in the set. Applications are e.g. in probabilistic graphical models and image processing. We prove NP hardness and a polynomial lower bound on the approximation factor, and upper bounds via four approximation algorithms based on different techniques. Our additional heuristics have attractive practical properties, e.g., to rely only on standard min-cut. Both our algorithms and heuristics appear to do well in practice.

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Jegelka, S., Bilmes, J. Cooperative Cuts: Graph Cuts with Submodular Edge Weights 24th European Conference on Operational Research (EURO XXIV), July 2010 (talk)

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BCI and robotics framework for stroke rehabilitation

Gomez Rodriguez, M., Grosse-Wentrup, M., Hill, J., Peters, J., Schölkopf, B., Gharabaghi, A.

4th International BCI Meeting, June 2010 (talk)

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Gomez Rodriguez, M., Grosse-Wentrup, M., Hill, J., Peters, J., Schölkopf, B., Gharabaghi, A. BCI and robotics framework for stroke rehabilitation 4th International BCI Meeting, June 2010 (talk)

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Solving Large-Scale Nonnegative Least Squares

Sra, S.

16th Conference of the International Linear Algebra Society (ILAS), June 2010 (talk)

Abstract

We study the fundamental problem of nonnegative least squares. This problem was apparently introduced by Lawson and Hanson [1] under the name NNLS. As is evident from its name, NNLS seeks least-squares solutions that are also nonnegative. Owing to its wide-applicability numerous algorithms have been derived for NNLS, beginning from the active-set approach of Lawson and Han- son [1] leading up to the sophisticated interior-point method of Bellavia et al. [2]. We present a new algorithm for NNLS that combines projected subgradients with the non-monotonic gradient descent idea of Barzilai and Borwein [3]. Our resulting algorithm is called BBSG, and we guarantee its convergence by ex- ploiting properties of NNLS in conjunction with projected subgradients. BBSG is surprisingly simple and scales well to large problems. We substantiate our claims by empirically evaluating BBSG and comparing it with established con- vex solvers and specialized NNLS algorithms. The numerical results suggest that BBSG is a practical method for solving large-scale NNLS problems.

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Sra, S. Solving Large-Scale Nonnegative Least Squares 16th Conference of the International Linear Algebra Society (ILAS), June 2010 (talk)

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Gaussian Mixture Modeling with Gaussian Process Latent Variable Models

Nickisch, H., Rasmussen, C.

Max Planck Institute for Biological Cybernetics, June 2010 (techreport)

Abstract

Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in a variety of complex data. The GPLVM consists of a set of points in a low dimensional latent space, and a stochastic map to the observed space. We show how it can be interpreted as a density model in the observed space. However, the GPLVM is not trained as a density model and therefore yields bad density estimates. We propose a new training strategy and obtain improved generalisation performance and better density estimates in comparative evaluations on several benchmark data sets.

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Nickisch, H., Rasmussen, C. Gaussian Mixture Modeling with Gaussian Process Latent Variable Models Max Planck Institute for Biological Cybernetics, June 2010 (techreport)

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Matrix Approximation Problems

Sra, S.

EU Regional School: Rheinisch-Westf{\"a}lische Technische Hochschule Aachen, May 2010 (talk)

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Sra, S. Matrix Approximation Problems EU Regional School: Rheinisch-Westf{\"a}lische Technische Hochschule Aachen, May 2010 (talk)

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BCI2000 and Python

Hill, NJ.

Invited lecture at the 7th International BCI2000 Workshop, Pacific Grove, CA, USA, May 2010 (talk)

Abstract

A tutorial, with exercises, on how to integrate your own Python code with the BCI2000 realtime software package.

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Hill, NJ. BCI2000 and Python Invited lecture at the 7th International BCI2000 Workshop, Pacific Grove, CA, USA, May 2010 (talk)

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Extending BCI2000 Functionality with Your Own C++ Code

Hill, NJ.

Invited lecture at the 7th International BCI2000 Workshop, Pacific Grove, CA, USA, May 2010 (talk)

Abstract

A tutorial, with exercises, on how to use BCI2000 C++ framework to write your own real-time signal-processing modules.

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Hill, NJ. Extending BCI2000 Functionality with Your Own C++ Code Invited lecture at the 7th International BCI2000 Workshop, Pacific Grove, CA, USA, May 2010 (talk)

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Generalized Proximity and Projection with Norms and Mixed-norms

Sra, S.

(192), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2010 (techreport)

Abstract

We discuss generalized proximity operators (GPO) and their associated generalized projection problems. On inputs of size n, we show how to efficiently apply GPOs and generalized projections for separable norms and distance-like functions to accuracy e in O(n log(1/e)) time. We also derive projection algorithms that run theoretically in O(n log n log(1/e)) time but can for suitable parameter ranges empirically outperform the O(n log(1/e)) projection method. The proximity and projection tasks are either separable, and solved directly, or are reduced to a single root-finding step. We highlight that as a byproduct, our analysis also yields an O(n log(1/e)) (weakly linear-time) procedure for Euclidean projections onto the l1;1-norm ball; previously only an O(n log n) method was known. We provide empirical evaluation to illustrate the performance of our methods, noting that for the l1;1-norm projection, our implementation is more than two orders of magnitude faster than the previously known method.

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Sra, S. Generalized Proximity and Projection with Norms and Mixed-norms (192), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2010 (techreport)

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Machine-Learning Methods for Decoding Intentional Brain States

Hill, NJ.

Symposium "Non-Invasive Brain Computer Interfaces: Current Developments and Applications" (BIOMAG), March 2010 (talk)

Abstract

Brain-computer interfaces (BCI) work by making the user perform a specific mental task, such as imagining moving body parts or performing some other covert mental activity, or attending to a particular stimulus out of an array of options, in order to encode their intention into a measurable brain signal. Signal-processing and machine-learning techniques are then used to decode the measured signal to identify the encoded mental state and hence extract the user&amp;lsquo;s initial intention. The high-noise high-dimensional nature of brain-signals make robust decoding techniques a necessity. Generally, the approach has been to use relatively simple feature extraction techniques, such as template matching and band-power estimation, coupled to simple linear classifiers. This has led to a prevailing view among applied BCI researchers that (sophisticated) machine-learning is irrelevant since it doesn&amp;lsquo;t matter what classifier you use once your features are extracted. Using examples from our own MEG and EEG experiments, I&amp;lsquo;ll demonstrate how machine-learning principles can be applied in order to improve BCI performance, if they are formulated in a domain-specific way. The result is a type of data-driven analysis that is more than just classification, and can be used to find better feature extractors.

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Hill, NJ. Machine-Learning Methods for Decoding Intentional Brain States Symposium "Non-Invasive Brain Computer Interfaces: Current Developments and Applications" (BIOMAG), March 2010 (talk)

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Cooperative Cuts: Graph Cuts with Submodular Edge Weights

Jegelka, S., Bilmes, J.

(189), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, March 2010 (techreport)

Abstract

We introduce a problem we call Cooperative cut, where the goal is to find a minimum-cost graph cut but where a submodular function is used to define the cost of a subsets of edges. That means, the cost of an edge that is added to the current cut set C depends on the edges in C. This generalization of the cost in the standard min-cut problem to a submodular cost function immediately makes the problem harder. Not only do we prove NP hardness even for nonnegative submodular costs, but also show a lower bound of Omega(|V|^(1/3)) on the approximation factor for the problem. On the positive side, we propose and compare four approximation algorithms with an overall approximation factor of min { |V|/2, |C*|, O( sqrt(|E|) log |V|), |P_max|}, where C* is the optimal solution, and P_max is the longest s, t path across the cut between given s, t. We also introduce additional heuristics for the problem which have attractive properties from the perspective of practical applications and implementations in that existing fast min-cut libraries may be used as subroutines. Both our approximation algorithms, and our heuristics, appear to do well in practice.

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Jegelka, S., Bilmes, J. Cooperative Cuts: Graph Cuts with Submodular Edge Weights (189), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, March 2010 (techreport)

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PAC-Bayesian Analysis in Unsupervised Learning

Seldin, Y.

Foundations and New Trends of PAC Bayesian Learning Workshop, March 2010 (talk)

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Seldin, Y. PAC-Bayesian Analysis in Unsupervised Learning Foundations and New Trends of PAC Bayesian Learning Workshop, March 2010 (talk)

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Learning Motor Primitives for Robotics

Kober, J., Peters, J.

EVENT Lab: Reinforcement Learning in Robotics and Virtual Reality, January 2010 (talk)

Abstract

The acquisition and self-improvement of novel motor skills is among the most important problems in robotics. Motor primitives offer one of the most promising frameworks for the application of machine learning techniques in this context. Employing the Dynamic Systems Motor primitives originally introduced by Ijspeert et al. (2003), appropriate learning algorithms for a concerted approach of both imitation and reinforcement learning are presented. Using these algorithms new motor skills, i.e., Ball-in-a-Cup, Ball-Paddling and Dart-Throwing, are learned.

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Kober, J., Peters, J. Learning Motor Primitives for Robotics EVENT Lab: Reinforcement Learning in Robotics and Virtual Reality, January 2010 (talk)

[BibTex]

Information-theoretic inference of common ancestors

Steudel, B., Ay, N.

Computing Research Repository (CoRR), abs/1010.5720, pages: 18, 2010 (techreport)

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Steudel, B., Ay, N. Information-theoretic inference of common ancestors Computing Research Repository (CoRR), abs/1010.5720, pages: 18, 2010 (techreport)

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2009

Learning an Interactive Segmentation System

Nickisch, H., Kohli, P., Rother, C.

Max Planck Institute for Biological Cybernetics, December 2009 (techreport)

Abstract

Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluated by computing the accuracy of their solutions under some fixed set of user interactions. This paper proposes a new evaluation and learning method which brings the user in the loop. It is based on the use of an active robot user - a simulated model of a human user. We show how this approach can be used to evaluate and learn parameters of state-of-the-art interactive segmentation systems. We also show how simulated user models can be integrated into the popular max-margin method for parameter learning and propose an algorithm to solve the resulting optimisation problem.

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2009

Nickisch, H., Kohli, P., Rother, C. Learning an Interactive Segmentation System Max Planck Institute for Biological Cybernetics, December 2009 (techreport)

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Machine Learning for Brain-Computer Interfaces

Hill, NJ.

Mini-Symposia on Assistive Machine Learning for People with Disabilities at NIPS (AMD), December 2009 (talk)

Abstract

Brain-computer interfaces (BCI) aim to be the ultimate in assistive technology: decoding a user‘s intentions directly from brain signals without involving any muscles or peripheral nerves. Thus, some classes of BCI potentially offer hope for users with even the most extreme cases of paralysis, such as in late-stage Amyotrophic Lateral Sclerosis, where nothing else currently allows communication of any kind. Other lines in BCI research aim to restore lost motor function in as natural a way as possible, reconnecting and in some cases re-training motor-cortical areas to control prosthetic, or previously paretic, limbs. Research and development are progressing on both invasive and non-invasive fronts, although BCI has yet to make a breakthrough to widespread clinical application. The high-noise high-dimensional nature of brain-signals, particularly in non-invasive approaches and in patient populations, make robust decoding techniques a necessity. Generally, the approach has been to use relatively simple feature extraction techniques, such as template matching and band-power estimation, coupled to simple linear classifiers. This has led to a prevailing view among applied BCI researchers that (sophisticated) machine-learning is irrelevant since "it doesn‘t matter what classifier you use once you‘ve done your preprocessing right and extracted the right features." I shall show a few examples of how this runs counter to both the empirical reality and the spirit of what needs to be done to bring BCI into clinical application. Along the way I‘ll highlight some of the interesting problems that remain open for machine-learners.

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Hill, NJ. Machine Learning for Brain-Computer Interfaces Mini-Symposia on Assistive Machine Learning for People with Disabilities at NIPS (AMD), December 2009 (talk)

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PAC-Bayesian Approach to Formulation of Clustering Objectives

Seldin, Y.

NIPS Workshop on "Clustering: Science or Art? Towards Principled Approaches", December 2009 (talk)

Abstract

Clustering is a widely used tool for exploratory data analysis. However, the theoretical understanding of clustering is very limited. We still do not have a well-founded answer to the seemingly simple question of "how many clusters are present in the data?", and furthermore a formal comparison of clusterings based on different optimization objectives is far beyond our abilities. The lack of good theoretical support gives rise to multiple heuristics that confuse the practitioners and stall development of the field. We suggest that the ill-posed nature of clustering problems is caused by the fact that clustering is often taken out of its subsequent application context. We argue that one does not cluster the data just for the sake of clustering it, but rather to facilitate the solution of some higher level task. By evaluation of the clustering‘s contribution to the solution of the higher level task it is possible to compare different clusterings, even those obtained by different optimization objectives. In the preceding work it was shown that such an approach can be applied to evaluation and design of co-clustering solutions. Here we suggest that this approach can be extended to other settings, where clustering is applied.

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Seldin, Y. PAC-Bayesian Approach to Formulation of Clustering Objectives NIPS Workshop on "Clustering: Science or Art? Towards Principled Approaches", December 2009 (talk)

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Semi-supervised Kernel Canonical Correlation Analysis of Human Functional Magnetic Resonance Imaging Data

Shelton, JA.

Women in Machine Learning Workshop (WiML), December 2009 (talk)

Abstract

Kernel Canonical Correlation Analysis (KCCA) is a general technique for subspace learning that incorporates principal components analysis (PCA) and Fisher linear discriminant analysis (LDA) as special cases. By finding directions that maximize correlation, KCCA learns representations tied more closely to underlying process generating the the data and can ignore high-variance noise directions. However, for data where acquisition in a given modality is expensive or otherwise limited, KCCA may suffer from small sample effects. We propose to use semi-supervised Laplacian regularization to utilize data that are present in only one modality. This manifold learning approach is able to find highly correlated directions that also lie along the data manifold, resulting in a more robust estimate of correlated subspaces. Functional magnetic resonance imaging (fMRI) acquired data are naturally amenable to subspace techniques as data are well aligned and such data of the human brain are a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single and multivariate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, Laplacian regularization improved performance whereas the semi-supervised variants of KCCA yielded the best performance. We additionally analyze the weights learned by the regression in order to infer brain regions that are important during different types of visual processing.

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Shelton, JA. Semi-supervised Kernel Canonical Correlation Analysis of Human Functional Magnetic Resonance Imaging Data Women in Machine Learning Workshop (WiML), December 2009 (talk)

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Detection of objects in noisy images and site percolation on square lattices

Langovoy, M., Wittich, O.

(2009-035), EURANDOM, Technische Universiteit Eindhoven, November 2009 (techreport)

Abstract

We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. Our procedure substantially differs from wavelets-based algorithms. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.

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Langovoy, M., Wittich, O. Detection of objects in noisy images and site percolation on square lattices (2009-035), EURANDOM, Technische Universiteit Eindhoven, November 2009 (techreport)

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An Incremental GEM Framework for Multiframe Blind Deconvolution, Super-Resolution, and Saturation Correction

Harmeling, S., Sra, S., Hirsch, M., Schölkopf, B.

(187), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

Abstract

We develop an incremental generalized expectation maximization (GEM) framework to model the multiframe blind deconvolution problem. A simplistic version of this problem was recently studied by Harmeling etal~cite{harmeling09}. We solve a more realistic version of this problem which includes the following major features: (i) super-resolution ability emph{despite} noise and unknown blurring; (ii) saturation-correction, i.e., handling of overexposed pixels that can otherwise confound the image processing; and (iii) simultaneous handling of color channels. These features are seamlessly integrated into our incremental GEM framework to yield simple but efficient multiframe blind deconvolution algorithms. We present technical details concerning critical steps of our algorithms, especially to highlight how all operations can be written using matrix-vector multiplications. We apply our algorithm to real-world images from astronomy and super resolution tasks. Our experimental results show that our methods yield improve d resolution and deconvolution at the same time.

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Harmeling, S., Sra, S., Hirsch, M., Schölkopf, B. An Incremental GEM Framework for Multiframe Blind Deconvolution, Super-Resolution, and Saturation Correction (187), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

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Efficient Filter Flow for Space-Variant Multiframe Blind Deconvolution

Hirsch, M., Sra, S., Schölkopf, B., Harmeling, S.

(188), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

Abstract

Ultimately being motivated by facilitating space-variant blind deconvolution, we present a class of linear transformations, that are expressive enough for space-variant filters, but at the same time especially designed for efficient matrix-vector-multiplications. Successful results on astronomical imaging through atmospheric turbulences and on noisy magnetic resonance images of constantly moving objects demonstrate the practical significance of our approach.

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Hirsch, M., Sra, S., Schölkopf, B., Harmeling, S. Efficient Filter Flow for Space-Variant Multiframe Blind Deconvolution (188), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

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Event-Related Potentials in Brain-Computer Interfacing

Hill, NJ.

Invited lecture on the bachelor & masters course "Introduction to Brain-Computer Interfacing", October 2009 (talk)

Abstract

An introduction to event-related potentials with specific reference to their use in brain-computer interfacing applications and research.

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Hill, NJ. Event-Related Potentials in Brain-Computer Interfacing Invited lecture on the bachelor & masters course "Introduction to Brain-Computer Interfacing", October 2009 (talk)

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BCI2000 and Python

Hill, NJ.

Invited lecture at the 5th International BCI2000 Workshop, October 2009 (talk)

Abstract

A tutorial, with exercises, on how to integrate your own Python code with the BCI2000 software package.

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Hill, NJ. BCI2000 and Python Invited lecture at the 5th International BCI2000 Workshop, October 2009 (talk)

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Implementing a Signal Processing Filter in BCI2000 Using C++

Hill, NJ., Mellinger, J.

Invited lecture at the 5th International BCI2000 Workshop, October 2009 (talk)

Abstract

This tutorial shows how the functionality of the BCI2000 software package can be extended with one‘s own code, using BCI2000‘s C++ API.

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Hill, NJ., Mellinger, J. Implementing a Signal Processing Filter in BCI2000 Using C++ Invited lecture at the 5th International BCI2000 Workshop, October 2009 (talk)

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Algebraic polynomials and moments of stochastic integrals

Langovoy, M.

(2009-031), EURANDOM, Technische Universiteit Eindhoven, October 2009 (techreport)

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Langovoy, M. Algebraic polynomials and moments of stochastic integrals (2009-031), EURANDOM, Technische Universiteit Eindhoven, October 2009 (techreport)

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Expectation Propagation on the Maximum of Correlated Normal Variables

Hennig, P.

Cavendish Laboratory: University of Cambridge, July 2009 (techreport)

Abstract

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities.

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Hennig, P. Expectation Propagation on the Maximum of Correlated Normal Variables Cavendish Laboratory: University of Cambridge, July 2009 (techreport)

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Consistent Nonparametric Tests of Independence

Gretton, A., Györfi, L.

(172), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2009 (techreport)

Abstract

Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when the empirical distribution of the variables is restricted to finite partitions. A third test statistic is defined as a kernel-based independence measure. Two kinds of tests are provided. Distribution-free strong consistent tests are derived on the basis of large deviation bounds on the test statistcs: these tests make almost surely no Type I or Type II error after a random sample size. Asymptotically alpha-level tests are obtained from the limiting distribution of the test statistics. For the latter tests, the Type I error converges to a fixed non-zero value alpha, and the Type II error drops to zero, for increasing sample size. All tests reject the null hypothesis of independence if the test statistics become large. The performance of the tests is evaluated experimentally on benchmark data.

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Gretton, A., Györfi, L. Consistent Nonparametric Tests of Independence (172), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2009 (techreport)

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Randomized algorithms for statistical image analysis based on percolation theory

Davies, P., Langovoy, M., Wittich, O.

27th European Meeting of Statisticians (EMS), July 2009 (talk)

Abstract

We propose a novel probabilistic method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation and random graph theories (see Grimmett (1999)). We address the problem of detection and estimation of signals in situations where the signal-to-noise ratio is particularly low. We present an algorithm that allows to detect objects of various shapes in noisy images. The algorithm has linear complexity and exponential accuracy. Our algorithm substantially diers from wavelets-based algorithms (see Arias-Castro et.al. (2005)). Moreover, we present an algorithm that produces a crude estimate of an object based on the noisy picture. This algorithm also has linear complexity and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedures.

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Davies, P., Langovoy, M., Wittich, O. Randomized algorithms for statistical image analysis based on percolation theory 27th European Meeting of Statisticians (EMS), July 2009 (talk)

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Learning Motor Primitives for Robotics

Kober, J., Peters, J., Oztop, E.

Advanced Telecommunications Research Center ATR, June 2009 (talk)

Abstract

[BibTex]

Kober, J., Peters, J., Oztop, E. Learning Motor Primitives for Robotics Advanced Telecommunications Research Center ATR, June 2009 (talk)

[BibTex]

Learning To Detect Unseen Object Classes by Between-Class Attribute Transfer

Lampert, C.

IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 2009 (talk)

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Lampert, C. Learning To Detect Unseen Object Classes by Between-Class Attribute Transfer IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 2009 (talk)

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Semi-supervised subspace analysis of human functional magnetic resonance imaging data

Shelton, J., Blaschko, M., Bartels, A.

(185), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2009 (techreport)

Abstract

Kernel Canonical Correlation Analysis is a very general technique for subspace learning that incorporates PCA and LDA as special cases. Functional magnetic resonance imaging (fMRI) acquired data is naturally amenable to these techniques as data are well aligned. fMRI data of the human brain is a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single- and multi-variate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, the semi-supervised variants of KCCA performed better than the supervised variants, including a supervised variant with Laplacian regularization. We additionally analyze the weights learned by the regression in order to infer brain regions that are important to different types of visual processing.

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Shelton, J., Blaschko, M., Bartels, A. Semi-supervised subspace analysis of human functional magnetic resonance imaging data (185), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2009 (techreport)

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Model selection, large deviations and consistency of data-driven tests

Langovoy, M.

(2009-007), EURANDOM, Technische Universiteit Eindhoven, March 2009 (techreport)

Abstract

We consider three general classes of data-driven statistical tests. Neyman's smooth tests, data-driven score tests and data-driven score tests for statistical inverse problems serve as important special examples for the classes of tests under consideration. Our tests are additionally incorporated with model selection rules. The rules are based on the penalization idea. Most of the optimal penalties, derived in statistical literature, can be used in our tests. We prove general consistency theorems for the tests from those classes. Our proofs make use of large deviations inequalities for deterministic and random quadratic forms. The paper shows that the tests can be applied for simple and composite parametric, semi- and nonparametric hypotheses. Applications to testing in statistical inverse problems and statistics for stochastic processes are also presented..

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Langovoy, M. Model selection, large deviations and consistency of data-driven tests (2009-007), EURANDOM, Technische Universiteit Eindhoven, March 2009 (techreport)

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2002

Kernel Dependency Estimation

Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V.

(98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)

Abstract

We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. Output kernels also make it possible to encode prior information and/or invariances in the loss function in an elegant way. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images.

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2002

Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V. Kernel Dependency Estimation (98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)

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Global Geometry of SVM Classifiers

Zhou, D., Xiao, B., Zhou, H., Dai, R.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)

Abstract

We construct an geometry framework for any norm Support Vector Machine (SVM) classifiers. Within this framework, separating hyperplanes, dual descriptions and solutions of SVM classifiers are constructed by a purely geometric fashion. In contrast with the optimization theory used in SVM classifiers, we have no complicated computations any more. Each step in our theory is guided by elegant geometric intuitions.

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Zhou, D., Xiao, B., Zhou, H., Dai, R. Global Geometry of SVM Classifiers Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)

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