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JMLR
2010

On the relation between universality, characteristic kernels and RKHS embedding of measures

9 years 9 months ago
On the relation between universality, characteristic kernels and RKHS embedding of measures
Universal kernels have been shown to play an important role in the achievability of the Bayes risk by many kernel-based algorithms that include binary classification, regression, etc. In this paper, we propose a notion of universality that generalizes the notions introduced by Steinwart and Micchelli et al. and study the necessary and sufficient conditions for a kernel to be universal. We show that all these notions of universality are closely linked to the injective embedding of a certain class of Borel measures into a reproducing kernel Hilbert space (RKHS). By exploiting this relation between universality and the embedding of Borel measures into an RKHS, we establish the relation between universal and characteristic kernels. The latter have been proposed in the context of the RKHS embedding of probability measures, used in statistical applications like homogeneity testing, independence testing, etc.
Bharath K. Sriperumbudur, Kenji Fukumizu, Gert R.
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JMLR
Authors Bharath K. Sriperumbudur, Kenji Fukumizu, Gert R. G. Lanckriet
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