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  Injective Hilbert Space Embeddings of Probability Measures

Sriperumbudur, B., Gretton, A., Fukumizu, K., Lanckriet, G., & Schölkopf, B. (2008). Injective Hilbert Space Embeddings of Probability Measures. In R. Servedio, & T. Zhang (Eds.), 21st Annual Conference on Learning Theory (COLT 2008) (pp. 111-122). Madison, WI, USA: Omnipress.

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Datensatz-Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-C83D-C Versions-Permalink: https://hdl.handle.net/21.11116/0000-0003-3D85-3
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 Urheber:
Sriperumbudur, BK, Autor           
Gretton, A1, 2, Autor           
Fukumizu, K, Autor           
Lanckriet, G, Autor
Schölkopf, B1, 2, Autor           
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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Schlagwörter: -
 Zusammenfassung: A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity
testing and independence testing. This embedding
represents any probability measure as a mean element
in a reproducing kernel Hilbert space (RKHS).
The embedding function has been proven to be injective
when the reproducing kernel is universal.
In this case, the embedding induces a metric on the
space of probability distributions defined on compact
metric spaces.
In the present work, we consider more broadly the
problem of specifying characteristic kernels, defined
as kernels for which the RKHS embedding
of probability measures is injective. In particular,
characteristic kernels can include non-universal kernels.
We restrict ourselves to translation-invariant
kernels on Euclidean space, and define the associated
metric on probability measures in terms of
the Fourier spectrum of the kernel and characteristic
functions of these measures. The support of the
kernel spectrum is important in finding whether a
kernel is characteristic: in particular, the embedding
is injective if and only if the kernel spectrum
has the entire domain as its support. Characteristic
kernels may nonetheless have difficulty in distinguishing
certain distributions on the basis of finite
samples, again due to the interaction of the kernel
spectrum and the characteristic functions of the
measures.

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 Datum: 2008-07
 Publikationsstatus: Erschienen
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 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: BibTex Citekey: 5122
 Art des Abschluß: -

Veranstaltung

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Titel: 21st Annual Conference on Learning Theory (COLT 2008)
Veranstaltungsort: Helsinki, Finland
Start-/Enddatum: 2008-07-09 - 2008-07-12

Entscheidung

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Titel: 21st Annual Conference on Learning Theory (COLT 2008)
Genre der Quelle: Konferenzband
 Urheber:
Servedio, RA, Herausgeber
Zhang, T, Herausgeber
Affiliations:
-
Ort, Verlag, Ausgabe: Madison, WI, USA : Omnipress
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 111 - 122 Identifikator: ISBN: 978-1-60558-205-4