Distances and dependence measures with reproducing kernel Hilbert spaces

  • Kenji Fukumizu (The Institute of Statistical Mathematics, Tokyo, Japan)
University n.n. Universität Leipzig (Leipzig)


I discuss a family of distances on the probability measures based on positive definite kernels and the associated reproducing kernel Hilbert spaces (RKHS). It is shown that, with an appropriate choice of a RKHS, the mean of the kernel in RKHS with respect to a probability uniquely determines the probability. With RKHS of this characteristic property, a distance on the probabilities can be defined as the distances of the means. This type of distances provides straightforward estimators with finite sample, unlike some other well-known distances on probabilities. Some statistical asymptotic results on the estimators are discussed. It is also easy to derive a dependence measure based on the distance by considering the distance between the joint probability and the product of the marginals. I will discuss a normalized dependence measure with positive definite kernel, and show an interesting relation with the conventional chi-square divergence.

02.08.10 06.08.10

Information Geometry and its Applications III

Universität Leipzig (Leipzig) University n.n. University n.n.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences, Germany

Paolo Gibilisco

Università degli Studi di Roma "Tor Vergata", Italy

František Matúš

Academy of Sciences of the Czech Republic, Czech Republic