Characteristic Kernels on Groups and Semigroups
2009
Conference Paper
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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) |
Event Name: | 22nd Annual Conference on Neural Information Processing Systems (NIPS 2008) |
Event Place: | Vancouver, BC, Canada |
Address: | Red Hook, NY, USA |
Digital: | 0 |
ISBN: | 978-1-605-60949-2 |
Language: | en |
Organization: | Max-Planck-Gesellschaft |
School: | Biologische Kybernetik |
Links: |
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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}, doi = {}, month_numeric = {6} } |