Information Geometry and its Applications III

Abstract Kenji Fukumizu

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Kenji Fukumizu  (The Institute of Statistical Mathematics, Japan)
Thursday, August 05, 2010, room Hörsaal 1
Distances and dependence measures with reproducing kernel Hilbert spaces

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.

Date and Location

August 02 - 06, 2010
University of Leipzig
04103 Leipzig

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
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František Matúš
Academy of Sciences of the Czech Republic
Institute of Information Theory and Automation
Czech Republic
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Scientific Committee

Shun-ichi Amari
Brain Science Institute, Mathematical Neuroscience Laboratory
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
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Administrative Contact

Antje Vandenberg
Max Planck Institute for Mathematics in the Sciences
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Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42