Characteristic kernels on groups and semigroups

Kenji Fukumizu, Bharath Sriperumbudur, Arthur Gretton, Bernhard Schölkopf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

45 Scopus citations

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 ℝ n. 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 ℝ + n.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
Pages473-480
Number of pages8
StatePublished - Dec 1 2009
Event22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada
Duration: Dec 8 2008Dec 11 2008

Publication series

NameAdvances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

Other

Other22nd Annual Conference on Neural Information Processing Systems, NIPS 2008
CountryCanada
CityVancouver, BC
Period12/8/0812/11/08

All Science Journal Classification (ASJC) codes

  • Information Systems

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