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Characteristic Kernels on Groups and Semigroups

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Sriperumbudur,  BK
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
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. In D. Koller, D. Schuurmans, Y. Bengio, & L. Bottou (Eds.), Advances in neural information processing systems 21 (pp. 473-480). Red Hook, NY, USA: Curran.


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+.