Publications | Max Planck Institute for Intelligent Systems

35 results (View BibTeX file of all listed publications)

2016

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Screening Rules for Convex Problems

Raj, A., Olbrich, J., Gärtner, B., Schölkopf, B., Jaggi, M.

2016 (unpublished) Submitted

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2016

ei Raj, A., Olbrich, J., Gärtner, B., Schölkopf, B., Jaggi, M. Screening Rules for Convex Problems 2016 (unpublished) Submitted

2010

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Computationally efficient algorithms for statistical image processing: Implementation in R

Langovoy, M., Wittich, O.

(2010-053), EURANDOM, Technische Universiteit Eindhoven, December 2010 (techreport)

Abstract

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

ei 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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ei 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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A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering

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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PDF Web [BibTex]

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

PDF Web [BibTex]

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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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ei 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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ei 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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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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ei 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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ei 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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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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ei 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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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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ei 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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Generalized Proximity and Projection with Norms and Mixed-norms

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

2008

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Frequent Subgraph Retrieval in Geometric Graph Databases

Nowozin, S., Tsuda, K.

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

Abstract

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

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2008

ei Nowozin, S., Tsuda, K. Frequent Subgraph Retrieval in Geometric Graph Databases (180), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2008 (techreport)

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Simultaneous Implicit Surface Reconstruction and Meshing

Giesen, J., Maier, M., Schölkopf, B.

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

Abstract

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

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ei Giesen, J., Maier, M., Schölkopf, B. Simultaneous Implicit Surface Reconstruction and Meshing (179), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2008 (techreport)

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Taxonomy Inference Using Kernel Dependence Measures

Blaschko, M., Gretton, A.

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

Abstract

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

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ei Blaschko, M., Gretton, A. Taxonomy Inference Using Kernel Dependence Measures (181), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2008 (techreport)

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

Seeger, M., Nickisch, H.

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

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ei Seeger, M., Nickisch, H. Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models (175), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2008 (techreport)

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Block-Iterative Algorithms for Non-Negative Matrix Approximation

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

Abstract

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

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ei Sra, S. Block-Iterative Algorithms for Non-Negative Matrix Approximation (176), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2008 (techreport)

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Approximation Algorithms for Bregman Clustering Co-clustering and Tensor Clustering

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

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

Abstract

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

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ei Sra, S., Jegelka, S., Banerjee, A. Approximation Algorithms for Bregman Clustering Co-clustering and Tensor Clustering (177), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2008 (techreport)

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Combining Appearance and Motion for Human Action Classification in Videos

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

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

Abstract

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

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ei Dhillon, P., Nowozin, S., Lampert, C. Combining Appearance and Motion for Human Action Classification in Videos (174), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, August 2008 (techreport)

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

Kim, K., Kwon, Y.

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

Abstract

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

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ei Kim, K., Kwon, Y. Example-based Learning for Single-image Super-resolution and JPEG Artifact Removal (173), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, August 2008 (techreport)

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

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

Abstract

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

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ei Chiappa, S. Unsupervised Bayesian Time-series Segmentation based on Linear Gaussian State-space Models (171), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, June 2008 (techreport)

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

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

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

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ei Kim, D., Sra, S., Dhillon, I. A New Non-monotonic Gradient Projection Method for the Non-negative Least Squares Problem (TR-08-28), University of Texas, Austin, TX, USA, June 2008 (techreport)

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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.

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ei Sra, S., Kim, D., Schölkopf, B. Non-monotonic Poisson Likelihood Maximization (170), Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2008 (techreport)

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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.

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ei Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., Smola, A. A Kernel Method for the Two-sample Problem (157), Max-Planck-Institute for Biological Cybernetics Tübingen, April 2008 (techreport)

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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.

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ei Hein, M., Steinke, F., Schölkopf, B. Energy Functionals for Manifold-valued Mappings and Their Properties (167), Max Planck Institute for Biological Cybernetics, Tübingen, January 2008 (techreport)

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Biologically Inspired Polymer Micro-Patterned Adhesives

Cheung, E., Sitti, M.

EDGEWOOD CHEMICAL BIOLOGICAL CENTER ABERDEEN PROVING GROUND MD, 2008 (techreport)

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pi Cheung, E., Sitti, M. Biologically Inspired Polymer Micro-Patterned Adhesives EDGEWOOD CHEMICAL BIOLOGICAL CENTER ABERDEEN PROVING GROUND MD, 2008 (techreport)

2005

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Popper, Falsification and the VC-dimension

Corfield, D., Schölkopf, B., Vapnik, V.

(145), Max Planck Institute for Biological Cybernetics, November 2005 (techreport)

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2005

ei Corfield, D., Schölkopf, B., Vapnik, V. Popper, Falsification and the VC-dimension (145), Max Planck Institute for Biological Cybernetics, November 2005 (techreport)

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A Combinatorial View of Graph Laplacians

(144), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2005 (techreport)

Abstract

Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties to Laplacian operators on continuous manifolds. There is still no strong proof on convergence for the normalized Laplacian. In this paper, we analyze different variants of graph Laplacians directly from the ways solving the original graph partitioning problem. The graph partitioning problem is a well-known combinatorial NP hard optimization problem. The spectral solutions provide evidence that normalized Laplacian encodes more reasonable considerations for graph partitioning. We also provide some examples to show their differences.

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ei Huang, J. A Combinatorial View of Graph Laplacians (144), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2005 (techreport)

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Beyond Pairwise Classification and Clustering Using Hypergraphs

Zhou, D., Huang, J., Schölkopf, B.

(143), Max Planck Institute for Biological Cybernetics, August 2005 (techreport)

Abstract

In many applications, relationships among objects of interest are more complex than pairwise. Simply approximating complex relationships as pairwise ones can lead to loss of information. An alternative for these applications is to analyze complex relationships among data directly, without the need to first represent the complex relationships into pairwise ones. A natural way to describe complex relationships is to use hypergraphs. A hypergraph is a graph in which edges can connect more than two vertices. Thus we consider learning from a hypergraph, and develop a general framework which is applicable to classification and clustering for complex relational data. We have applied our framework to real-world web classification problems and obtained encouraging results.

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ei Zhou, D., Huang, J., Schölkopf, B. Beyond Pairwise Classification and Clustering Using Hypergraphs (143), Max Planck Institute for Biological Cybernetics, August 2005 (techreport)

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Measuring Statistical Dependence with Hilbert-Schmidt Norms

Gretton, A., Bousquet, O., Smola, A., Schölkopf, B.

(140), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2005 (techreport)

Abstract

We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

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ei Gretton, A., Bousquet, O., Smola, A., Schölkopf, B. Measuring Statistical Dependence with Hilbert-Schmidt Norms (140), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2005 (techreport)

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Approximate Inference for Robust Gaussian Process Regression

Kuss, M., Pfingsten, T., Csato, L., Rasmussen, C.

(136), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract

Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectation-propagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectation-propagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling.

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ei Kuss, M., Pfingsten, T., Csato, L., Rasmussen, C. Approximate Inference for Robust Gaussian Process Regression (136), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

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Maximum-Margin Feature Combination for Detection and Categorization

BakIr, G., Wu, M., Eichhorn, J.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract

In this paper we are concerned with the optimal combination of features of possibly different types for detection and estimation tasks in machine vision. We propose to combine features such that the resulting classifier maximizes the margin between classes. In contrast to existing approaches which are non-convex and/or generative we propose to use a discriminative model leading to convex problem formulation and complexity control. Furthermore we assert that decision functions should not compare apples and oranges by comparing features of different types directly. Instead we propose to combine different similarity measures for each different feature type. Furthermore we argue that the question: Which feature type is more discriminative for task X? is ill-posed and show empirically that the answer to this question might depend on the complexity of the decision function.

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ei BakIr, G., Wu, M., Eichhorn, J. Maximum-Margin Feature Combination for Detection and Categorization Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

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Towards a Statistical Theory of Clustering. Presented at the PASCAL workshop on clustering, London

von Luxburg, U., Ben-David, S.

Presented at the PASCAL workshop on clustering, London, 2005 (techreport)

Abstract

The goal of this paper is to discuss statistical aspects of clustering in a framework where the data to be clustered has been sampled from some unknown probability distribution. Firstly, the clustering of the data set should reveal some structure of the underlying data rather than model artifacts due to the random sampling process. Secondly, the more sample points we have, the more reliable the clustering should be. We discuss which methods can and cannot be used to tackle those problems. In particular we argue that generalization bounds as they are used in statistical learning theory of classification are unsuitable in a general clustering framework. We suggest that the main replacements of generalization bounds should be convergence proofs and stability considerations. This paper should be considered as a road map paper which identifies important questions and potentially fruitful directions for future research about statistical clustering. We do not attempt to present a complete statistical theory of clustering.

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ei von Luxburg, U., Ben-David, S. Towards a Statistical Theory of Clustering. Presented at the PASCAL workshop on clustering, London Presented at the PASCAL workshop on clustering, London, 2005 (techreport)

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Approximate Bayesian Inference for Psychometric Functions using MCMC Sampling

Kuss, M., Jäkel, F., Wichmann, F.

(135), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract

In psychophysical studies the psychometric function is used to model the relation between the physical stimulus intensity and the observer's ability to detect or discriminate between stimuli of different intensities. In this report we propose the use of Bayesian inference to extract the information contained in experimental data estimate the parameters of psychometric functions. Since Bayesian inference cannot be performed analytically we describe how a Markov chain Monte Carlo method can be used to generate samples from the posterior distribution over parameters. These samples are used to estimate Bayesian confidence intervals and other characteristics of the posterior distribution. In addition we discuss the parameterisation of psychometric functions and the role of prior distributions in the analysis. The proposed approach is exemplified using artificially generate d data and in a case study for real experimental data. Furthermore, we compare our approach with traditional methods based on maximum-likelihood parameter estimation combined with bootstrap techniques for confidence interval estimation. The appendix provides a description of an implementation for the R environment for statistical computing and provides the code for reproducing the results discussed in the experiment section.

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ei Kuss, M., Jäkel, F., Wichmann, F. Approximate Bayesian Inference for Psychometric Functions using MCMC Sampling (135), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems

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