English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  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.

Item is

Files

show Files
hide Files
:
COLT-2008-Sriperumbudur.pdf (Any fulltext), 318KB
Name:
COLT-2008-Sriperumbudur.pdf
Description:
-
OA-Status:
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show
hide
Locator:
http://colt2008.cs.helsinki.fi/ (Table of contents)
Description:
-
OA-Status:

Creators

show
hide
 Creators:
Sriperumbudur, BK, Author           
Gretton, A1, 2, Author           
Fukumizu, K, Author           
Lanckriet, G, Author
Schölkopf, B1, 2, Author           
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              

Content

show
hide
Free keywords: -
 Abstract: 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.

Details

show
hide
Language(s):
 Dates: 2008-07
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 5122
 Degree: -

Event

show
hide
Title: 21st Annual Conference on Learning Theory (COLT 2008)
Place of Event: Helsinki, Finland
Start-/End Date: 2008-07-09 - 2008-07-12

Legal Case

show

Project information

show

Source 1

show
hide
Title: 21st Annual Conference on Learning Theory (COLT 2008)
Source Genre: Proceedings
 Creator(s):
Servedio, RA, Editor
Zhang, T, Editor
Affiliations:
-
Publ. Info: Madison, WI, USA : Omnipress
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 111 - 122 Identifier: ISBN: 978-1-60558-205-4