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Characteristic Kernels on Groups and Semigroups

2009

Conference Paper

ei


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+.

Author(s): Fukumizu, K. and Sriperumbudur, BK. and Gretton, A. and Schölkopf, B.
Book Title: Advances in neural information processing systems 21
Journal: Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008
Pages: 473-480
Year: 2009
Month: June
Day: 0
Editors: D Koller and D Schuurmans and Y Bengio and L Bottou
Publisher: Curran

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Address: Red Hook, NY, USA
Digital: 0
Event Name: 22nd Annual Conference on Neural Information Processing Systems (NIPS 2008)
Event Place: Vancouver, BC, Canada
ISBN: 978-1-605-60949-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5466,
  title = {Characteristic Kernels on Groups and Semigroups},
  author = {Fukumizu, K. and Sriperumbudur, BK. and Gretton, A. and Sch{\"o}lkopf, B.},
  journal = {Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008},
  booktitle = {Advances in neural information processing systems 21},
  pages = {473-480},
  editors = {D Koller and D Schuurmans and Y Bengio and L Bottou},
  publisher = {Curran},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Red Hook, NY, USA},
  month = jun,
  year = {2009},
  month_numeric = {6}
}