Characteristic Kernels on Groups and Semigroups (2009)
Fukumizu, K., Sriperumbudur, B.K., Gretton, A., Schölkopf, B.
Embeddings of random variables in reproducing kernel Hilbert spaces (RKHSs) may be used to conduct statistical inference based on higher order moments. For sufficiently rich (characteristic) RKHSs,...
Kernel Methods for Detecting the Direction of Time Series (2009)
Peters, J., Janzing, D., Gretton, A., Schölkopf, B.
We propose two kernel based methods for detecting the time direction in empirical time series. First we apply a Support Vector Machine on the finitedimensional distributions of the time series...
Covariate Shift and Local Learning by Distribution Matching (2009)
Gretton, A., Smola, A.J., Huang, J., Schmittfull, M., Borgwardt, K.M., Schölkopf, B.
Given sets of observations of training and test data, we consider the problem of re-weighting the training data such that its distribution more closely matches that of the test data. We achieve this...
Kernel Measures of Conditional Dependence (2008)
Fukumizu, K., Gretton, A., Sun, X., Schölkopf, B.
We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence...
A Kernel Statistical Test of Independence (2008)
Gretton, A., Fukumizu, K., Teo, C.H., Song, L., Schölkopf, B., Smola, A.J.
Whereas kernel measures of independence have been widely applied in machine learning (notably in kernel ICA), there is as yet no method to determine whether they have detected statistically...
RKHS Representation of Measures Applied to Homogeneity, Independence, and Fourier Optics (2008)
Schölkopf, B., Sriperumbudur, B.K., Gretton, A., Fukumizu, K.
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Tailoring density estimation via reproducing kernel moment matching (2008)
Song, L., Zhang, X., Smola, A., Gretton, A., Schölkopf, B.
Moment matching is a popular means of parametric density estimation. We extend this technique to nonparametric estimation of mixture models. Our approach works by embedding distributions into a...
Injective Hilbert Space Embeddings of Probability Measures (2008)
Sriperumbudur, B.K., Gretton, A., Fukumizu, K., Lanckriet, G., Schölkopf, B.
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing and independence testing. This embedding...
Belitski, A., Gretton, A., Magri, C., Murayama, Y., Montemurro, M.A., Logothetis, N.K., ...
Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode...
Gretton, A., Macke, J., Logothetis, N.K.
Pattern recognition methods have shown that functional magnetic resonance imaging (fMRI) data can reveal significant information about brain activity. For example, in the debate of how object...
Inferring Spike Trains From Local Field Potentials (2008)
Rasch, M.J., Gretton, A., Murayama, Y., Maass, W., Logothetis, N.K.
We investigated whether it is possible to infer spike trains solely on the basis of the underlying local field potentials (LFPs). Using support vector machines and linear regression models, we found...
A Hilbert-Schmidt Dependence Maximization Approach to Unsupervised Structure Discovery (2008)
In recent work by (Song et al., 2007), it has been proposed to perform clustering by maximizing a Hilbert-Schmidt independence criterion with respect to a predefined cluster structure Y , by solving...
Semi-Supervised Laplacian Regularization of Kernel Canonical Correlation Analysis (2008)
Blaschko, M.B., Lampert, C.H., Gretton, A., Daelemans, W., Goethals, B., Morik, K.
Kernel canonical correlation analysis (KCCA) is a dimensionality reduction technique for paired data. By finding directions that maximize correlation, KCCA learns representations that are more...
Kernel Measures of Conditional Dependence (2008)
Fukumizu, K., Gretton, A., Sun, X., Schölkopf, B., Platt, J. C., Koller, D., ...
We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence...
A Kernel Statistical Test of Independence (2008)
Gretton, A., Fukumizu, K., Teo, C.H., Song, L., Schölkopf, B., Smola, A.J., ...
Whereas kernel measures of independence have been widely applied in machine learning (notably in kernel ICA), there is as yet no method to determine whether they have detected statistically...
Nonparametric Independence Tests: Space Partitioning and Kernel Approaches (2008)
Gretton, A., Györfi, L., Freund, Y., Györfi, L., Turán, G., Zeugmann, T.
Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when...
RKHS Representation of Measures Applied to Homogeneity, Independence, and Fourier Optics (2008)
Schölkopf, B., Sriperumbudur, B.K., Gretton, A., Fukumizu, K., Jetter, K., Smale, S., ...
Colored Maximum Variance Unfolding (2008)
Song, L., Smola, A.J., Borgwardt, K., Gretton, A., Platt, J. C., Koller, D., ...
Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximizing the variance of their embeddings while...
Tailoring density estimation via reproducing kernel moment matching (2008)
Song, L., Zhang, X., Smola, A., Gretton, A., Schölkopf, B., Cohen, W. W., ...
Moment matching is a popular means of parametric density estimation. We extend this technique to nonparametric estimation of mixture models. Our approach works by embedding distributions into a...
Injective Hilbert Space Embeddings of Probability Measures (2008)
Sriperumbudur, B.K., Gretton, A., Fukumizu, K., Lanckriet, G., Schölkopf, B., Servedio, R. A., ...
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing and independence testing. This embedding...
Nonparametric Independence Tests: Space Partitioning and Kernel Approaches. (2008)
Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when...
Gene selection via the BAHSIC family of algorithms (2007)
Song, L., Bedo, J., Borgwardt, K.M., Gretton, A., Smola, A.
Motivation: Identifying significant genes among thousands of sequences on a microarray is a central challenge for cancer research in bioinformatics. The ultimate goal is to detect the genes that are...
Statistical Consistency of Kernel Canonical Correlation Analysis (2007)
Fukumizu, K., Bach, F.R., Gretton, A.
While kernel canonical correlation analysis (CCA) has been applied in many contexts, the convergence of finite sample estimates of the associated functions to their population counterparts has not...
Supervised Feature Selection via Dependence Estimation (2007)
Song, L., Smola, A.J., Gretton, A., Borgwardt, K.M., Bedo, J.
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...
A Dependence Maximization View of Clustering (2007)
Song, L., Smola, A.J., Gretton, A., Borgwardt, K.M.
We propose a family of clustering algorithms based on the maximization of dependence between the input variables and their cluster labels, as expressed by the Hilbert-Schmidt Independence Criterion...
A Hilbert Space Embedding for Distributions (2007)
Smola, A., Gretton, A., Song, L., Schölkopf, B., Hutter, M., Servedio, R. A., ...
We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert...
Fast Kernel ICA using an Approximate Newton Method (2007)
Shen, H., Jegelka, S., Gretton, A.
Recent approaches to independent component analysis (ICA) have used kernel independence measures to obtain very good performance, particularly where classical methods experience difficulty (for...
Correcting Sample Selection Bias by Unlabeled Data (2007)
Huang, J., Smola, A., Gretton, A., Borgwardt, K.M., Schölkopf, B.
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...
A Kernel Method for the Two-Sample-Problem (2007)
Gretton, A., Borgwardt, K.M., Rasch, M., Schölkopf, B., Smola, A.
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...
A Kernel Approach to Comparing Distributions (2007)
Gretton, A., Borgwardt, K.M., Rasch, M., Schölkopf, B., Smola, A.J.
We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a Reproducing Kernel Hilbert...
Invited Review Correcting for the Sampling Bias Problem in Spike Train Information Measures (2007)
Stefano Panzeri, Riccardo Senatore, Marcelo A. Montemurro, Rasmus S, M. J. Rasch, A. Gretton, ...
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Statistical Convergence of Kernel CCA (2006)
Fukumizu, K., Bach, F., Gretton, A.
While kernel canonical correlation analysis (kernel CCA) has been applied in many problems, the asymptotic convergence of the functions estimated from a finite sample to the true functions has not...
The effect of artifacts on dependence measurement in fMRI (2006)
Gretton, A., Belitski, A., Murayama, Y., Schölkopf, B., Logothetis, N.K.
Integrating structured biological data by Kernel Maximum Mean Discrepancy (2006)
Borgwardt, K., Gretton, A., Rasch, M., Schölkopf, B., Smola, A.
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...
Measuring Statistical Dependence with Hilbert-Schmidt Norms (2005)
Gretton, A., Bousquet, O., Smola, A., Schoelkopf, B.
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...
An Online Support Vector Machine for Abnormal Events Detection (2005)
Davy, M., Desobry, F., Gretton, A., Doncarli, C.
The ability to detect online abnormal events in signals is essential in many real-world Signal Processing applications. Previous algorithms require an explicit signal statistical model, and interpret...
Kernel Constrained Covariance for Dependence Measurement (2005)
Gretton, A., Smola, A.J., Bousquet, O., Herbrich, R., Belitski, A., Augath, M., ...
We discuss reproducing kernel Hilbert space (RKHS)-based measures of statistical dependence, with emphasis on constrained covariance (COCO), a novel criterion to test dependence of random variables....
Kernel Methods for Measuring Independence (2005)
Gretton, A., Herbrich, R., Smola, A., Bousquet, O., Schölkopf, B.
We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the...
Ranking on Data Manifolds (2004)
Zhou,D., Weston,J., Gretton,A., Bousquet,O., Schölkopf,B.
The Google search engine has enjoyed a huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a...
Multivariate Regression via Stiefel Manifold Constraints (2004)
Bakir,G.H., Gretton,A., Franz,M.O., Schölkopf,B.
We introduce a learning technique for regression between high-dimensional spaces. Standard methods typically reduce this task to many one-dimensional problems, with each output dimension considered...
Ranking on Data Manifolds (2004)
Zhou, D., Weston, J., Gretton, A., Bousquet, O., Schölkopf, B., Thrun, S., ...
The Google search engine has enjoyed a huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a...
Multivariate Regression via Stiefel Manifold Constraints (2004)
Bakir, G.H., Gretton, A., Franz, M.O., Schölkopf, B., Rasmussen, C. E., Bülthoff, H. H., ...
We introduce a learning technique for regression between high-dimensional spaces. Standard methods typically reduce this task to many one-dimensional problems, with each output dimension considered...