@inproceedings{5122,
  title = {Injective Hilbert Space Embeddings of Probability Measures},
  journal = {Proceedings of the 21st Annual Conference on Learning Theory (COLT 2008)},
  booktitle = {Proceedings of the 21st Annual Conference on Learning Theory},
  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.},
  pages = {111-122},
  editors = {RA Servedio and T Zhang},
  publisher = {Omnipress},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Madison, WI, USA},
  month = jul,
  year = {2008},
  slug = {5122},
  author = {Sriperumbudur, BK. and Gretton, A. and Fukumizu, K. and Lanckriet, G. and Sch{\"o}lkopf, B.},
  month_numeric = {7}
}