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Characteristic Kernels on Groups and Semigroups

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83923

Fukumizu,  K
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84233

Sriperumbudur,  BK
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Dept. Empirical Inference, Max Planck Institute for Intelligent System, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83946

Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Fukumizu, K., Sriperumbudur, B., Gretton, A., & Schölkopf, B. (2009). Characteristic Kernels on Groups and Semigroups. Advances in neural information processing systems 21: 22nd Annual Conference on Neural Information Processing Systems 2008, 473-480.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C471-7
Abstract
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, each probability distribution has a unique embedding, allowing all statistical properties of the distribution to be taken into consideration. Necessary and sufficient conditions for an RKHS to be characteristic exist for Rn. In the present work, conditions are established for an RKHS to be characteristic on groups and semigroups. Illustrative examples are provided, including characteristic kernels on periodic domains, rotation matrices, and Rn+.