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- Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, Alexander J. Smola
- Journal of Machine Learning Research
- 2012

We propose a framework for analyzing and comparing distributions, which we use to construct 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), and is called the maximum mean discrepancy… (More)

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… (More)

We consider the scenario where training and test data are drawn from different distributions, commonly referred to as sample selection bias. Most algorithms for this setting try to first recover sampling distributions and then make appropriate corrections based on the distribution estimate. We present a nonparametric method which directly produces… (More)

- Nino Shervashidze, Pascal Schweitzer, Erik Jan van Leeuwen, Kurt Mehlhorn, Karsten M. Borgwardt
- Journal of Machine Learning Research
- 2011

In this article, we propose a family of efficient kernels for large graphs with discrete node labels. Key to our method is a rapid feature extraction scheme based on the Weisfeiler-Lehman test of isomorphism on graphs. It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information. A family of kernels can… (More)

- Jun Cao, Korbinian Schneeberger, +14 authors Detlef Weigel
- Nature genetics
- 2011

The plant Arabidopsis thaliana occurs naturally in many different habitats throughout Eurasia. As a foundation for identifying genetic variation contributing to adaptation to diverse environments, a 1001 Genomes Project to sequence geographically diverse A. thaliana strains has been initiated. Here we present the first phase of this project, based on… (More)

MOTIVATION
Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based statistical test for this problem, based on the fact that two distributions are different if and only if there exists at least one function having different expectation… (More)

- Claude Becker, Jörg Hagmann, +4 authors Detlef Weigel
- Nature
- 2011

Heritable epigenetic polymorphisms, such as differential cytosine methylation, can underlie phenotypic variation. Moreover, wild strains of the plant Arabidopsis thaliana differ in many epialleles, and these can influence the expression of nearby genes. However, to understand their role in evolution, it is imperative to ascertain the emergence rate and… (More)

- Karsten M. Borgwardt, Hans-Peter Kriegel
- Fifth IEEE International Conference on Data…
- 2005

Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are… (More)

State-of-the-art graph kernels do not scale to large graphs with hundreds of nodes and thousands of edges. In this article we propose to compare graphs by counting graphlets, i.e., subgraphs with k nodes where k ∈ {3, 4, 5}. Exhaustive enumeration of all graphlets being prohibitively expensive, we introduce two theoretically grounded speedup schemes, one… (More)

We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between the features and the labels. The key idea is that good features should maximise such dependence. Feature selection for various supervised learning problems (including classification and regression) is unified… (More)