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 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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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...
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...
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., ...
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...
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...
Parameter estimation for von MisesFisher distributions (2007)
Tanabe, A., Fukumizu, K., Oba, S., Takenouchi, T., Ishii, S.
When analyzing high-dimensional data, it is often appropriate to pay attention only to the direction of each datum, disregarding its norm. The von MisesFisher (vMF) distribution is a natural...
A kernel-based causal learning algorithm (2007)
Sun, X., Janzing, D., Schölkopf, B., Fukumizu, K.
We describe a causal learning method, which employs measuring the strength of statistical dependences in terms of the Hilbert-Schmidt norm of kernel-based cross-covariance operators. Following the...
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...
Statistical Convergence of Kernel CCA (2005)
Fukumizu, K, Bach, F, Gretton, Arthur
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...