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2008


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Partitioning of Image Datasets using Discriminative Context Information

Lampert, CH.

In CVPR 2008, pages: 1-8, IEEE Computer Society, Los Alamitos, CA, USA, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 2008 (inproceedings)

Abstract
We propose a new method to partition an unlabeled dataset, called Discriminative Context Partitioning (DCP). It is motivated by the idea of splitting the dataset based only on how well the resulting parts can be separated from a context class of disjoint data points. This is in contrast to typical clustering techniques like K-means that are based on a generative model by implicitly or explicitly searching for modes in the distribution of samples. The discriminative criterion in DCP avoids the problems that density based methods have when the a priori assumption of multimodality is violated, when the number of samples becomes small in relation to the dimensionality of the feature space, or if the cluster sizes are strongly unbalanced. We formulate DCP‘s separation property as a large-margin criterion, and show how the resulting optimization problem can be solved efficiently. Experiments on the MNIST and USPS datasets of handwritten digits and on a subset of the Caltech256 dataset show that, given a suitable context, DCP can achieve good results even in situation where density-based clustering techniques fail.

PDF Web DOI [BibTex]

2008

PDF Web DOI [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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Bayesian online multi-task learning using regularization networks

Pillonetto, G., Dinuzzo, F., De Nicolao, G.

In pages: 4517-4522, IEEE Service Center, Piscataway, NJ, USA, 2008 American Control Conference (ACC), June 2008 (inproceedings)

Abstract
Recently, standard single-task kernel methods have been extended to the case of multi-task learning under the framework of regularization. Experimental results have shown that such an approach can perform much better than single-task techniques, especially when few examples per task are available. However, a possible drawback may be computational complexity. For instance, when using regularization networks, complexity scales as the cube of the overall number of data associated with all the tasks. In this paper, an efficient computational scheme is derived for a widely applied class of multi-task kernels. More precisely, a quadratic loss is assumed and the multi-task kernel is the sum of a common term and a task-specific one. The proposed algorithm performs online learning recursively updating the estimates as new data become available. The learning problem is formulated in a Bayesian setting. The optimal estimates are obtained by solving a sequence of subproblems which involve projection of random variables onto suitable subspaces. The algorithm is tested on a simulated data set.

Web DOI [BibTex]

Web DOI [BibTex]


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Correlational Spectral Clustering

Blaschko, MB., Lampert, CH.

In CVPR 2008, pages: 1-8, IEEE Computer Society, Los Alamitos, CA, USA, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 2008 (inproceedings)

Abstract
We present a new method for spectral clustering with paired data based on kernel canonical correlation analysis, called correlational spectral clustering. Paired data are common in real world data sources, such as images with text captions. Traditional spectral clustering algorithms either assume that data can be represented by a single similarity measure, or by co-occurrence matrices that are then used in biclustering. In contrast, the proposed method uses separate similarity measures for each data representation, and allows for projection of previously unseen data that are only observed in one representation (e.g. images but not text). We show that this algorithm generalizes traditional spectral clustering algorithms and show consistent empirical improvement over spectral clustering on a variety of datasets of images with associated text.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Approximate Dynamic Programming with Gaussian Processes

Deisenroth, M., Peters, J., Rasmussen, C.

In ACC 2008, pages: 4480-4485, IEEE Service Center, Piscataway, NJ, USA, 2008 American Control Conference, June 2008 (inproceedings)

Abstract
In general, it is difficult to determine an optimal closed-loop policy in nonlinear control problems with continuous-valued state and control domains. Hence, approximations are often inevitable. The standard method of discretizing states and controls suffers from the curse of dimensionality and strongly depends on the chosen temporal sampling rate. In this paper, we introduce Gaussian process dynamic programming (GPDP) and determine an approximate globally optimal closed-loop policy. In GPDP, value functions in the Bellman recursion of the dynamic programming algorithm are modeled using Gaussian processes. GPDP returns an optimal statefeedback for a finite set of states. Based on these outcomes, we learn a possibly discontinuous closed-loop policy on the entire state space by switching between two independently trained Gaussian processes. A binary classifier selects one Gaussian process to predict the optimal control signal. We show that GPDP is able to yield an almost optimal solution to an LQ problem using few sample points. Moreover, we successfully apply GPDP to the underpowered pendulum swing up, a complex nonlinear control problem.

PDF Web [BibTex]

PDF Web [BibTex]


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Beyond Sliding Windows: Object Localization by Efficient Subwindow Search

Lampert, C., Blaschko, M., Hofmann, T.

In CVPR 2008, pages: 1-8, IEEE Computer Society, Los Alamitos, CA, USA, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 2008, Best paper award (inproceedings)

Abstract
Most successful object recognition systems rely on binary classification, deciding only if an object is present or not, but not providing information on the actual object location. To perform localization, one can take a sliding window approach, but this strongly increases the computational cost, because the classifier function has to be evaluated over a large set of candidate subwindows. In this paper, we propose a simple yet powerful branchand- bound scheme that allows efficient maximization of a large class of classifier functions over all possible subimages. It converges to a globally optimal solution typically in sublinear time. We show how our method is applicable to different object detection and retrieval scenarios. The achieved speedup allows the use of classifiers for localization that formerly were considered too slow for this task, such as SVMs with a spatial pyramid kernel or nearest neighbor classifiers based on the 2-distance. We demonstrate state-of-the-art performance of the resulting systems on the UIUC Cars dataset, the PASCAL VOC 2006 dataset and in the PASCAL VOC 2007 competition.

PDF PDF Web DOI [BibTex]

PDF PDF Web DOI [BibTex]


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Computed Torque Control with Nonparametric Regression Models

Nguyen-Tuong, D., Seeger, M., Peters, J.

In ACC 2008, pages: 212-217, IEEE Service Center, Piscataway, NJ, USA, 2008 American Control Conference, June 2008 (inproceedings)

Abstract
Computed torque control allows the design of considerably more precise, energy-efficient and compliant controls for robots. However, the major obstacle is the requirement of an accurate model for torque generation, which cannot be obtained in some cases using rigid-body formulations due to unmodeled nonlinearities, such as complex friction or actuator dynamics. In such cases, models approximated from robot data present an appealing alternative. In this paper, we compare two nonparametric regression methods for model approximation, i.e., locally weighted projection regression (LWPR) and Gaussian process regression (GPR). While locally weighted regression was employed for real-time model estimation in learning adaptive control, Gaussian process regression has not been used in control to-date due to high computational requirements. The comparison includes the assessment of model approximation for both regression methods using data originated from SARCOS robot arm, as well as an evaluation of the robot tracking p erformance in computed torque control employing the approximated models. Our results show that GPR can be applied for real-time control achieving higher accuracy. However, for the online learning LWPR is superior by reason of lower computational requirements.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Multi-Classification by Categorical Features via Clustering

Seldin, Y., Tishby, N.

In In the proceedings of the 25th International Conference on Machine Learning (ICML 2008), pages: 920-927, 25th International Conference on Machine Learning (ICML), June 2008 (inproceedings)

Abstract
We derive a generalization bound for multi-classification schemes based on grid clustering in categorical parameter product spaces. Grid clustering partitions the parameter space in the form of a Cartesian product of partitions for each of the parameters. The derived bound provides a means to evaluate clustering solutions in terms of the generalization power of a built-on classifier. For classification based on a single feature the bound serves to find a globally optimal classification rule. Comparison of the generalization power of individual features can then be used for feature ranking. Our experiments show that in this role the bound is much more precise than mutual information or normalized correlation indices.

PDF Web [BibTex]

PDF Web [BibTex]


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A Kernel Test of Nonlinear Granger Causality

Sun, X.

In Proceedings of the Workshop on Inference and Estimation in Probabilistic Time-Series Models, pages: 79-89, (Editors: Barber, D. , A. T. Cemgil, S. Chiappa), Isaac Newton Institute for Mathematical Sciences, Cambridge, United Kingdom, Workshop on Inference and Estimation in Probabilistic Time-Series Models, June 2008 (inproceedings)

Abstract
We present a novel test of nonlinear Granger causality in bivariate time series. The trace norm of conditional covariance operators is used to capture the prediction errors. Based on this measure, a subsampling-based multiple testing procedure tests the prediction improvement of one time series by the other one. The distributional properties of the resulting p-values reveal the direction of Granger causality. Encouraging results of experiments with simulated and real-world data support our approach.

PDF [BibTex]

PDF [BibTex]


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Thin-Plate Splines Between Riemannian Manifolds

Steinke, F., Hein, M., Schölkopf, B.

Workshop on Geometry and Statistics of Shapes, June 2008 (talk)

Abstract
With the help of differential geometry we describe a framework to define a thin-plate spline like energy for maps between arbitrary Riemannian manifolds. The so-called Eells energy only depends on the intrinsic geometry of the input and output manifold, but not on their respective representation. The energy can then be used for regression between manifolds, we present results for cases where the outputs are rotations, sets of angles, or points on 3D surfaces. In the future we plan to also target regression where the output is an element of "shape space", understood as a Riemannian manifold. One could also further explore the meaning of the Eells energy when applied to diffeomorphisms between shapes, especially with regard to its potential use as a distance measure between shapes that does not depend on the embedding or the parametrisation of the shapes.

Web [BibTex]

Web [BibTex]


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Bayesian Color Constancy Revisited

Gehler, P., Rother, C., Blake, A., Minka, T., Sharp, T.

In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR, June 2008, http://dx.doi.org/10.1109/CVPR.2008.4587765 (inproceedings)

website+code+data pdf [BibTex]

website+code+data pdf [BibTex]


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Real-time Learning of Resolved Velocity Control on a Mitsubishi PA-10

Peters, J., Nguyen-Tuong, D.

In ICRA 2008, pages: 2872-2877, IEEE Service Center, Piscataway, NJ, USA, 2008 IEEE International Conference on Robotics and Automation, May 2008 (inproceedings)

Abstract
Learning inverse kinematics has long been fascinating the robot learning community. While humans acquire this transformation to complicated tool spaces with ease, it is not a straightforward application for supervised learning algorithms due to non-convex learning problem. However, the key insight that the problem can be considered convex in small local regions allows the application of locally linear learning methods. Nevertheless, the local solution of the problem depends on the data distribution which can result into inconsistent global solutions with large model discontinuities. While this problem can be treated in various ways in offline learning, it poses a serious problem for online learning. Previous approaches to the real-time learning of inverse kinematics avoid this problem using smart data generation, such as the learner biasses its own solution. Such biassed solutions can result into premature convergence, and from the resulting solution it is often hard to understand what has been learned in tha t local region. This paper improves and solves this problem by presenting a learning algorithm which can deal with this inconsistency through re-weighting the data online. Furthermore, we show that our algorithms work not only in simulation, but we present real-time learning results on a physical Mitsubishi PA-10 robot arm.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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State Space Compression with Predictive Representations

Boularias, A., Izadi, M., Chaib-Draa, B.

In Flairs 2008, pages: 41-46, (Editors: Wilson, D. C., H. C. Lane), AAAI Press, Menlo Park, CA, USA, 21st International Florida Artificial Intelligence Research Society Conference, May 2008 (inproceedings)

Abstract
Current studies have demonstrated that the representational power of predictive state representations (PSRs) is at least equal to the one of partially observable Markov decision processes (POMDPs). This is while early steps in planning and generalization with PSRs suggest substantial improvements compared to POMDPs. However, lack of practical algorithms for learning these representations severely restricts their applicability. The computational inefficiency of exact PSR learning methods naturally leads to the exploration of various approximation methods that can provide a good set of core tests through less computational effort. In this paper, we address this problem in an optimization framework. In particular, our approach aims to minimize the potential error that may be caused by missing a number of core tests. We provide analysis of the error caused by this compression and present an empirical evaluation illustrating the performance of this approach.

PDF Web [BibTex]

PDF Web [BibTex]


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Learning resolved velocity control

Peters, J.

2008 IEEE International Conference on Robotics and Automation (ICRA), May 2008 (talk)

Web [BibTex]

Web [BibTex]


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Bayesian methods for protein structure determination

Habeck, M.

Machine Learning in Structural Bioinformatics, April 2008 (talk)

Web [BibTex]

Web [BibTex]


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Graph Mining with Variational Dirichlet Process Mixture Models

Tsuda, K., Kurihara, K.

In SDM 2008, pages: 432-442, (Editors: Zaki, M. J.), Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 8th SIAM International Conference on Data Mining, April 2008 (inproceedings)

Abstract
Graph data such as chemical compounds and XML documents are getting more common in many application domains. A main difficulty of graph data processing lies in the intrinsic high dimensionality of graphs, namely, when a graph is represented as a binary feature vector of indicators of all possible subgraph patterns, the dimensionality gets too large for usual statistical methods. We propose a nonparametric Bayesian method for clustering graphs and selecting salient patterns at the same time. Variational inference is adopted here, because sampling is not applicable due to extremely high dimensionality. The feature set minimizing the free energy is efficiently collected with the DFS code tree, where the generation of useless subgraphs is suppressed by a tree pruning condition. In experiments, our method is compared with a simpler approach based on frequent subgraph mining, and graph kernels.

PDF Web [BibTex]

PDF 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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Model-Based Reinforcement Learning with Continuous States and Actions

Deisenroth, M., Rasmussen, C., Peters, J.

In ESANN 2008, pages: 19-24, (Editors: Verleysen, M. ), d-side, Evere, Belgium, European Symposium on Artificial Neural Networks, April 2008 (inproceedings)

Abstract
Finding an optimal policy in a reinforcement learning (RL) framework with continuous state and action spaces is challenging. Approximate solutions are often inevitable. GPDP is an approximate dynamic programming algorithm based on Gaussian process (GP) models for the value functions. In this paper, we extend GPDP to the case of unknown transition dynamics. After building a GP model for the transition dynamics, we apply GPDP to this model and determine a continuous-valued policy in the entire state space. We apply the resulting controller to the underpowered pendulum swing up. Moreover, we compare our results on this RL task to a nearly optimal discrete DP solution in a fully known environment.

PDF Web [BibTex]

PDF Web [BibTex]


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Learning Inverse Dynamics: A Comparison

Nguyen-Tuong, D., Peters, J., Seeger, M., Schölkopf, B.

In Advances in Computational Intelligence and Learning: Proceedings of the European Symposium on Artificial Neural Networks, pages: 13-18, (Editors: M Verleysen), d-side, Evere, Belgium, 16th European Symposium on Artificial Neural Networks (ESANN), April 2008 (inproceedings)

Abstract
While it is well-known that model can enhance the control performance in terms of precision or energy efficiency, the practical application has often been limited by the complexities of manually obtaining sufficiently accurate models. In the past, learning has proven a viable alternative to using a combination of rigid-body dynamics and handcrafted approximations of nonlinearities. However, a major open question is what nonparametric learning method is suited best for learning dynamics? Traditionally, locally weighted projection regression (LWPR), has been the standard method as it is capable of online, real-time learning for very complex robots. However, while LWPR has had significant impact on learning in robotics, alternative nonparametric regression methods such as support vector regression (SVR) and Gaussian processes regression (GPR) offer interesting alternatives with fewer open parameters and potentially higher accuracy. In this paper, we evaluate these three alternatives for model learning. Our comparison consists out of the evaluation of learning quality for each regression method using original data from SARCOS robot arm, as well as the robot tracking performance employing learned models. The results show that GPR and SVR achieve a superior learning precision and can be applied for real-time control obtaining higher accuracy. However, for the online learning LWPR presents the better method due to its lower computational requirements.

PDF Web [BibTex]

PDF Web [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]

2006


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Global Biclustering of Microarray Data

Wolf, T., Brors, B., Hofmann, T., Georgii, E.

In ICDMW 2006, pages: 125-129, (Editors: Tsumoto, S. , C. W. Clifton, N. Zhong, X. Wu, J. Liu, B. W. Wah, Y.-M. Cheung), IEEE Computer Society, Los Alamitos, CA, USA, Sixth IEEE International Conference on Data Mining, December 2006 (inproceedings)

Abstract
We consider the problem of simultaneously clustering genes and conditions of a gene expression data matrix. A bicluster is defined as a subset of genes that show similar behavior within a subset of conditions. Finding biclusters can be useful for revealing groups of genes involved in the same molecular process as well as groups of conditions where this process takes place. Previous work either deals with local, bicluster-based criteria or assumes a very specific structure of the data matrix (e.g. checkerboard or block-diagonal) [11]. In contrast, our goal is to find a set of flexibly arranged biclusters which is optimal in regard to a global objective function. As this is a NP-hard combinatorial problem, we describe several techniques to obtain approximate solutions. We benchmarked our approach successfully on the Alizadeh B-cell lymphoma data set [1].

Web DOI [BibTex]

2006

Web DOI [BibTex]


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Conformal Multi-Instance Kernels

Blaschko, M., Hofmann, T.

In NIPS 2006 Workshop on Learning to Compare Examples, pages: 1-6, NIPS Workshop on Learning to Compare Examples, December 2006 (inproceedings)

Abstract
In the multiple instance learning setting, each observation is a bag of feature vectors of which one or more vectors indicates membership in a class. The primary task is to identify if any vectors in the bag indicate class membership while ignoring vectors that do not. We describe here a kernel-based technique that defines a parametric family of kernels via conformal transformations and jointly learns a discriminant function over bags together with the optimal parameter settings of the kernel. Learning a conformal transformation effectively amounts to weighting regions in the feature space according to their contribution to classification accuracy; regions that are discriminative will be weighted higher than regions that are not. This allows the classifier to focus on regions contributing to classification accuracy while ignoring regions that correspond to vectors found both in positive and in negative bags. We show how parameters of this transformation can be learned for support vector machines by posing the problem as a multiple kernel learning problem. The resulting multiple instance classifier gives competitive accuracy for several multi-instance benchmark datasets from different domains.

PDF Web [BibTex]

PDF Web [BibTex]


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A Kernel Method for the Two-Sample-Problem

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

20th Annual Conference on Neural Information Processing Systems (NIPS), December 2006 (talk)

Abstract
We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a reproducing kernel Hilbert space (RKHS). The first test is based on a large deviation bound for the test statistic, while the second is based on the asymptotic distribution of this statistic. We show that the test statistic can be computed in $O(m^2)$ time. We apply our approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where our test performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.

PDF [BibTex]

PDF [BibTex]


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Ab-initio gene finding using machine learning

Schweikert, G., Zeller, G., Zien, A., Ong, C., de Bona, F., Sonnenburg, S., Phillips, P., Rätsch, G.

NIPS Workshop on New Problems and Methods in Computational Biology, December 2006 (talk)

Web [BibTex]

Web [BibTex]


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Reinforcement Learning by Reward-Weighted Regression

Peters, J.

NIPS Workshop: Towards a New Reinforcement Learning? , December 2006 (talk)

Web [BibTex]

Web [BibTex]


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Graph boosting for molecular QSAR analysis

Saigo, H., Kadowaki, T., Kudo, T., Tsuda, K.

NIPS Workshop on New Problems and Methods in Computational Biology, December 2006 (talk)

Abstract
We propose a new boosting method that systematically combines graph mining and mathematical programming-based machine learning. Informative and interpretable subgraph features are greedily found by a series of graph mining calls. Due to our mathematical programming formulation, subgraph features and pre-calculated real-valued features are seemlessly integrated. We tested our algorithm on a quantitative structure-activity relationship (QSAR) problem, which is basically a regression problem when given a set of chemical compounds. In benchmark experiments, the prediction accuracy of our method favorably compared with the best results reported on each dataset.

Web [BibTex]

Web [BibTex]


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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]

PDF [BibTex]


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Inferring Causal Directions by Evaluating the Complexity of Conditional Distributions

Sun, X., Janzing, D., Schölkopf, B.

NIPS Workshop on Causality and Feature Selection, December 2006 (talk)

Abstract
We propose a new approach to infer the causal structure that has generated the observed statistical dependences among n random variables. The idea is that the factorization of the joint measure of cause and effect into P(cause)P(effect|cause) leads typically to simpler conditionals than non-causal factorizations. To evaluate the complexity of the conditionals we have tried two methods. First, we have compared them to those which maximize the conditional entropy subject to the observed first and second moments since we consider the latter as the simplest conditionals. Second, we have fitted the data with conditional probability measures being exponents of functions in an RKHS space and defined the complexity by a Hilbert-space semi-norm. Such a complexity measure has several properties that are useful for our purpose. We describe some encouraging results with both methods applied to real-world data. Moreover, we have combined constraint-based approaches to causal discovery (i.e., methods using only information on conditional statistical dependences) with our method in order to distinguish between causal hypotheses which are equivalent with respect to the imposed independences. Furthermore, we compare the performance to Bayesian approaches to causal inference.

Web [BibTex]


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Information-theoretic Metric Learning

Davis, J., Kulis, B., Sra, S., Dhillon, I.

In NIPS 2006 Workshop on Learning to Compare Examples, pages: 1-5, NIPS Workshop on Learning to Compare Examples, December 2006 (inproceedings)

Abstract
We formulate the metric learning problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. Via a surprising equivalence, we show that this problem can be solved as a low-rank kernel learning problem. Specifically, we minimize the Burg divergence of a low-rank kernel to an input kernel, subject to pairwise distance constraints. Our approach has several advantages over existing methods. First, we present a natural information-theoretic formulation for the problem. Second, the algorithm utilizes the methods developed by Kulis et al. [6], which do not involve any eigenvector computation; in particular, the running time of our method is faster than most existing techniques. Third, the formulation offers insights into connections between metric learning and kernel learning.

PDF Web [BibTex]

PDF Web [BibTex]


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Pattern Mining in Frequent Dynamic Subgraphs

Borgwardt, KM., Kriegel, H-P., Wackersreuther, P.

In pages: 818-822, (Editors: Clifton, C.W.), IEEE Computer Society, Los Alamitos, CA, USA, Sixth International Conference on Data Mining (ICDM), December 2006 (inproceedings)

Abstract
Graph-structured data is becoming increasingly abundant in many application domains. Graph mining aims at finding interesting patterns within this data that represent novel knowledge. While current data mining deals with static graphs that do not change over time, coming years will see the advent of an increasing number of time series of graphs. In this article, we investigate how pattern mining on static graphs can be extended to time series of graphs. In particular, we are considering dynamic graphs with edge insertions and edge deletions over time. We define frequency in this setting and provide algorithmic solutions for finding frequent dynamic subgraph patterns. Existing subgraph mining algorithms can be easily integrated into our framework to make them handle dynamic graphs. Experimental results on real-world data confirm the practical feasibility of our approach.

Web DOI [BibTex]

Web DOI [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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Learning Optimal EEG Features Across Time, Frequency and Space

Farquhar, J., Hill, J., Schölkopf, B.

NIPS Workshop on Current Trends in Brain-Computer Interfacing, December 2006 (talk)

PDF Web [BibTex]

PDF Web [BibTex]


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Semi-Supervised Learning

Zien, A.

Advanced Methods in Sequence Analysis Lectures, November 2006 (talk)

Web [BibTex]

Web [BibTex]


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3DString: a feature string kernel for 3D object classification on voxelized data

Assfalg, J., Borgwardt, KM., Kriegel, H-P.

In pages: 198-207, (Editors: Yu, P.S. , V.J. Tsotras, E.A. Fox, B. Liu), ACM Press, New York, NY, USA, 15th ACM International Conference on Information and Knowledge Management (CIKM), November 2006 (inproceedings)

Abstract
Classification of 3D objects remains an important task in many areas of data management such as engineering, medicine or biology. As a common preprocessing step in current approaches to classification of voxelized 3D objects, voxel representations are transformed into a feature vector description.In this article, we introduce an approach of transforming 3D objects into feature strings which represent the distribution of voxels over the voxel grid. Attractively, this feature string extraction can be performed in linear runtime with respect to the number of voxels. We define a similarity measure on these feature strings that counts common k-mers in two input strings, which is referred to as the spectrum kernel in the field of kernel methods. We prove that on our feature strings, this similarity measure can be computed in time linear to the number of different characters in these strings. This linear runtime behavior makes our kernel attractive even for large datasets that occur in many application domains. Furthermore, we explain that our similarity measure induces a metric which allows to combine it with an M-tree for handling of large volumes of data. Classification experiments on two published benchmark datasets show that our novel approach is competitive with the best state-of-the-art methods for 3D object classification.

DOI [BibTex]

DOI [BibTex]


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Adapting Spatial Filter Methods for Nonstationary BCIs

Tomioka, R., Hill, J., Blankertz, B., Aihara, K.

In IBIS 2006, pages: 65-70, 2006 Workshop on Information-Based Induction Sciences, November 2006 (inproceedings)

Abstract
A major challenge in applying machine learning methods to Brain-Computer Interfaces (BCIs) is to overcome the possible nonstationarity in the data from the datablock the method is trained on and that the method is applied to. Assuming the joint distributions of the whitened signal and the class label to be identical in two blocks, where the whitening is done in each block independently, we propose a simple adaptation formula that is applicable to a broad class of spatial filtering methods including ICA, CSP, and logistic regression classifiers. We characterize the class of linear transformations for which the above assumption holds. Experimental results on 60 BCI datasets show improved classification accuracy compared to (a) fixed spatial filter approach (no adaptation) and (b) fixed spatial pattern approach (proposed by Hill et al., 2006 [1]).

PDF [BibTex]

PDF [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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A Machine Learning Approach for Determining the PET Attenuation Map from Magnetic Resonance Images

Hofmann, M., Steinke, F., Judenhofer, M., Claussen, C., Schölkopf, B., Pichler, B.

IEEE Medical Imaging Conference, November 2006 (talk)

Abstract
A promising new combination in multimodality imaging is MR-PET, where the high soft tissue contrast of Magnetic Resonance Imaging (MRI) and the functional information of Positron Emission Tomography (PET) are combined. Although many technical problems have recently been solved, it is still an open problem to determine the attenuation map from the available MR scan, as the MR intensities are not directly related to the attenuation values. One standard approach is an atlas registration where the atlas MR image is aligned with the patient MR thus also yielding an attenuation image for the patient. We also propose another approach, which to our knowledge has not been tried before: Using Support Vector Machines we predict the attenuation value directly from the local image information. We train this well-established machine learning algorithm using small image patches. Although both approaches sometimes yielded acceptable results, they also showed their specific shortcomings: The registration often fails with large deformations whereas the prediction approach is problematic when the local image structure is not characteristic enough. However, the failures often do not coincide and integration of both information sources is promising. We therefore developed a combination method extending Support Vector Machines to use not only local image structure but also atlas registered coordinates. We demonstrate the strength of this combination approach on a number of examples.

[BibTex]

[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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Semi-Supervised Support Vector Machines and Application to Spam Filtering

Zien, A.

ECML Discovery Challenge Workshop, September 2006 (talk)

Abstract
After introducing the semi-supervised support vector machine (aka TSVM for "transductive SVM"), a few popular training strategies are briefly presented. Then the assumptions underlying semi-supervised learning are reviewed. Finally, two modern TSVM optimization techniques are applied to the spam filtering data sets of the workshop; it is shown that they can achieve excellent results, if the problem of the data being non-iid can be handled properly.

PDF Web [BibTex]


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A Linear Programming Approach for Molecular QSAR analysis

Saigo, H., Kadowaki, T., Tsuda, K.

In MLG 2006, pages: 85-96, (Editors: Gärtner, T. , G. C. Garriga, T. Meinl), International Workshop on Mining and Learning with Graphs, September 2006, Best Paper Award (inproceedings)

Abstract
Small molecules in chemistry can be represented as graphs. In a quantitative structure-activity relationship (QSAR) analysis, the central task is to find a regression function that predicts the activity of the molecule in high accuracy. Setting a QSAR as a primal target, we propose a new linear programming approach to the graph-based regression problem. Our method extends the graph classification algorithm by Kudo et al. (NIPS 2004), which is a combination of boosting and graph mining. Instead of sequential multiplicative updates, we employ the linear programming boosting (LP) for regression. The LP approach allows to include inequality constraints for the parameter vector, which turns out to be particularly useful in QSAR tasks where activity values are sometimes unavailable. Furthermore, the efficiency is improved significantly by employing multiple pricing.

PDF PDF [BibTex]

PDF PDF [BibTex]


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Incremental Aspect Models for Mining Document Streams

Surendran, A., Sra, S.

In PKDD 2006, pages: 633-640, (Editors: Fürnkranz, J. , T. Scheffer, M. Spiliopoulou), Springer, Berlin, Germany, 10th European Conference on Principles and Practice of Knowledge Discovery in Databases, September 2006 (inproceedings)

Abstract
In this paper we introduce a novel approach for incrementally building aspect models, and use it to dynamically discover underlying themes from document streams. Using the new approach we present an application which we call “query-line tracking” i.e., we automatically discover and summarize different themes or stories that appear over time, and that relate to a particular query. We present evaluation on news corpora to demonstrate the strength of our method for both query-line tracking, online indexing and clustering.

Web DOI [BibTex]

Web DOI [BibTex]


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PALMA: Perfect Alignments using Large Margin Algorithms

Rätsch, G., Hepp, B., Schulze, U., Ong, C.

In GCB 2006, pages: 104-113, (Editors: Huson, D. , O. Kohlbacher, A. Lupas, K. Nieselt, A. Zell), Gesellschaft für Informatik, Bonn, Germany, German Conference on Bioinformatics, September 2006 (inproceedings)

Abstract
Despite many years of research on how to properly align sequences in the presence of sequencing errors, alternative splicing and micro-exons, the correct alignment of mRNA sequences to genomic DNA is still a challenging task. We present a novel approach based on large margin learning that combines kernel based splice site predictions with common sequence alignment techniques. By solving a convex optimization problem, our algorithm -- called PALMA -- tunes the parameters of the model such that the true alignment scores higher than all other alignments. In an experimental study on the alignments of mRNAs containing artificially generated micro-exons, we show that our algorithm drastically outperforms all other methods: It perfectly aligns all 4358 sequences on an hold-out set, while the best other method misaligns at least 90 of them. Moreover, our algorithm is very robust against noise in the query sequence: when deleting, inserting, or mutating up to 50% of the query sequence, it still aligns 95% of all sequences correctly, while other methods achieve less than 36% accuracy. For datasets, additional results and a stand-alone alignment tool see http://www.fml.mpg.de/raetsch/projects/palma.

PDF Web [BibTex]

PDF Web [BibTex]


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Graph Based Semi-Supervised Learning with Sharper Edges

Shin, H., Hill, N., Rätsch, G.

In ECML 2006, pages: 401-412, (Editors: Fürnkranz, J. , T. Scheffer, M. Spiliopoulou), Springer, Berlin, Germany, 17th European Conference on Machine Learning (ECML), September 2006 (inproceedings)

Abstract
In many graph-based semi-supervised learning algorithms, edge weights are assumed to be fixed and determined by the data points‘ (often symmetric)relationships in input space, without considering directionality. However, relationships may be more informative in one direction (e.g. from labelled to unlabelled) than in the reverse direction, and some relationships (e.g. strong weights between oppositely labelled points) are unhelpful in either direction. Undesirable edges may reduce the amount of influence an informative point can propagate to its neighbours -- the point and its outgoing edges have been ``blunted.‘‘ We present an approach to ``sharpening‘‘ in which weights are adjusted to meet an optimization criterion wherever they are directed towards labelled points. This principle can be applied to a wide variety of algorithms. In the current paper, we present one ad hoc solution satisfying the principle, in order to show that it can improve performance on a number of publicly available benchmark data sets.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Robust MEG Source Localization of Event Related Potentials: Identifying Relevant Sources by Non-Gaussianity

Breun, P., Grosse-Wentrup, M., Utschick, W., Buss, M.

In DAGM 2006, pages: 394-403, (Editors: Franke, K. , K.-R. Müller, B. Nickolay, R. Schäfer), Springer, Berlin, Germany, 28th Annual Symposium of the German Association for Pattern Recognition, September 2006 (inproceedings)

Abstract
Independent Component Analysis (ICA) is a frequently used preprocessing step in source localization of MEG and EEG data. By decomposing the measured data into maximally independent components (ICs), estimates of the time course and the topographies of neural sources are obtained. In this paper, we show that when using estimated source topographies for localization, correlations between neural sources introduce an error into the obtained source locations. This error can be avoided by reprojecting ICs onto the observation space, but requires the identification of relevant ICs. For Event Related Potentials (ERPs), we identify relevant ICs by estimating their non-Gaussianity. The efficacy of the approach is tested on auditory evoked potentials (AEPs) recorded by MEG. It is shown that ten trials are sufficient for reconstructing all important characteristics of the AEP, and source localization of the reconstructed ERP yields the same focus of activity as the average of 250 trials.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Finite-Horizon Optimal State-Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle

Deisenroth, MP., Ohtsuka, T., Weissel, F., Brunn, D., Hanebeck, UD.

In MFI 2006, pages: 371-376, (Editors: Hanebeck, U. D.), IEEE Service Center, Piscataway, NJ, USA, 6th IEEE International Conference on Multisensor Fusion and Integration, September 2006 (inproceedings)

Abstract
In this paper, an approach to the finite-horizon optimal state-feedback control problem of nonlinear, stochastic, discrete-time systems is presented. Starting from the dynamic programming equation, the value function will be approximated by means of Taylor series expansion up to second-order derivatives. Moreover, the problem will be reformulated, such that a minimum principle can be applied to the stochastic problem. Employing this minimum principle, the optimal control problem can be rewritten as a two-point boundary-value problem to be solved at each time step of a shrinking horizon. To avoid numerical problems, the two-point boundary-value problem will be solved by means of a continuation method. Thus, the curse of dimensionality of dynamic programming is avoided, and good candidates for the optimal state-feedback controls are obtained. The proposed approach will be evaluated by means of a scalar example system.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Uniform Convergence of Adaptive Graph-Based Regularization

Hein, M.

In COLT 2006, pages: 50-64, (Editors: Lugosi, G. , H.-U. Simon), Springer, Berlin, Germany, 19th Annual Conference on Learning Theory, September 2006 (inproceedings)

Abstract
The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying manifold structure and second to the density of the data-generating probability measure. We identify in this paper the limit of the regularizer and show uniform convergence over the space of Hoelder functions. As an intermediate step we derive upper bounds on the covering numbers of Hoelder functions on compact Riemannian manifolds, which are of independent interest for the theoretical analysis of manifold-based learning methods.

PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Efficient Large Scale Linear Programming Support Vector Machines

Sra, S.

In ECML 2006, pages: 767-774, (Editors: Fürnkranz, J. , T. Scheffer, M. Spiliopoulou), Springer, Berlin, Germany, 17th European Conference on Machine Learning, September 2006 (inproceedings)

Abstract
This paper presents a decomposition method for efficiently constructing ℓ1-norm Support Vector Machines (SVMs). The decomposition algorithm introduced in this paper possesses many desirable properties. For example, it is provably convergent, scales well to large datasets, is easy to implement, and can be extended to handle support vector regression and other SVM variants. We demonstrate the efficiency of our algorithm by training on (dense) synthetic datasets of sizes up to 20 million points (in ℝ32). The results show our algorithm to be several orders of magnitude faster than a previously published method for the same task. We also present experimental results on real data sets—our method is seen to be not only very fast, but also highly competitive against the leading SVM implementations.

Web DOI [BibTex]

Web DOI [BibTex]


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Regularised CSP for Sensor Selection in BCI

Farquhar, J., Hill, N., Lal, T., Schölkopf, B.

In Proceedings of the 3rd International Brain-Computer Interface Workshop and Training Course 2006, pages: 14-15, (Editors: GR Müller-Putz and C Brunner and R Leeb and R Scherer and A Schlögl and S Wriessnegger and G Pfurtscheller), Verlag der Technischen Universität Graz, Graz, Austria, 3rd International Brain-Computer Interface Workshop and Training Course, September 2006 (inproceedings)

Abstract
The Common Spatial Pattern (CSP) algorithm is a highly successful method for efficiently calculating spatial filters for brain signal classification. Spatial filtering can improve classification performance considerably, but demands that a large number of electrodes be mounted, which is inconvenient in day-to-day BCI usage. The CSP algorithm is also known for its tendency to overfit, i.e. to learn the noise in the training set rather than the signal. Both problems motivate an approach in which spatial filters are sparsified. We briefly sketch a reformulation of the problem which allows us to do this, using 1-norm regularisation. Focusing on the electrode selection issue, we present preliminary results on EEG data sets that suggest that effective spatial filters may be computed with as few as 10--20 electrodes, hence offering the potential to simplify the practical realisation of BCI systems significantly.

PDF PDF [BibTex]

PDF PDF [BibTex]


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Time-Dependent Demixing of Task-Relevant EEG Signals

Hill, N., Farquhar, J., Lal, T., Schölkopf, B.

In Proceedings of the 3rd International Brain-Computer Interface Workshop and Training Course 2006, pages: 20-21, (Editors: GR Müller-Putz and C Brunner and R Leeb and R Scherer and A Schlögl and S Wriessnegger and G Pfurtscheller), Verlag der Technischen Universität Graz, Graz, Austria, 3rd International Brain-Computer Interface Workshop and Training Course, September 2006 (inproceedings)

Abstract
Given a spatial filtering algorithm that has allowed us to identify task-relevant EEG sources, we present a simple approach for monitoring the activity of these sources while remaining relatively robust to changes in other (task-irrelevant) brain activity. The idea is to keep spatial *patterns* fixed rather than spatial filters, when transferring from training to test sessions or from one time window to another. We show that a fixed spatial pattern (FSP) approach, using a moving-window estimate of signal covariances, can be more robust to non-stationarity than a fixed spatial filter (FSF) approach.

PDF PDF [BibTex]

PDF PDF [BibTex]