Characteristic kernels on groups and semigroups

Kenji Fukumizu; Bharath Sriperumbudur; Arthur Gretton; Bernhard Schölkopf

Characteristic kernels on groups and semigroups

Kenji Fukumizu, Bharath Sriperumbudur, Arthur Gretton, Bernhard Schölkopf

Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

60 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 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 ℝ₊ⁿ.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
Publisher	Neural Information Processing Systems
Pages	473-480
Number of pages	8
ISBN (Print)	9781605609492
State	Published - 2009
Event	22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada Duration: Dec 8 2008 → Dec 11 2008

Publication series

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

Other

Other	22nd Annual Conference on Neural Information Processing Systems, NIPS 2008
Country/Territory	Canada
City	Vancouver, BC
Period	12/8/08 → 12/11/08

All Science Journal Classification (ASJC) codes

Information Systems

Cite this

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title = "Characteristic kernels on groups and semigroups",

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 ℝ+n.",

author = "Kenji Fukumizu and Bharath Sriperumbudur and Arthur Gretton and Bernhard Sch{\"o}lkopf",

year = "2009",

language = "English (US)",

isbn = "9781605609492",

series = "Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference",

publisher = "Neural Information Processing Systems",

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note = "22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 ; Conference date: 08-12-2008 Through 11-12-2008",

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Fukumizu, K, Sriperumbudur, B, Gretton, A & Schölkopf, B 2009, Characteristic kernels on groups and semigroups. in Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference, Neural Information Processing Systems, pp. 473-480, 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008, Vancouver, BC, Canada, 12/8/08.

Characteristic kernels on groups and semigroups. / Fukumizu, Kenji; Sriperumbudur, Bharath; Gretton, Arthur et al.
Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. Neural Information Processing Systems, 2009. p. 473-480 (Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Characteristic kernels on groups and semigroups

AU - Fukumizu, Kenji

AU - Sriperumbudur, Bharath

AU - Gretton, Arthur

AU - Schölkopf, Bernhard

PY - 2009

Y1 - 2009

N2 - 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 ℝ+n.

AB - 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 ℝ+n.

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M3 - Conference contribution

AN - SCOPUS:78049347967

SN - 9781605609492

T3 - Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

SP - 473

EP - 480

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

PB - Neural Information Processing Systems

T2 - 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008

Y2 - 8 December 2008 through 11 December 2008

ER -

Characteristic kernels on groups and semigroups

Abstract

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All Science Journal Classification (ASJC) codes

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