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

Bharath K. Sriperumbudur, Kenji Fukumizu, Gert R.G. Lanckriet

Research output: Contribution to journalConference articlepeer-review

34 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)773-780
Number of pages8
JournalJournal of Machine Learning Research
StatePublished - 2010
Event13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010 - Sardinia, Italy
Duration: May 13 2010May 15 2010

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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