

Information Geometry and its Applications III
Abstract Johannes Rauh
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Johannes Rauh (Max Planck Institute for Mathematics in the Sciences, Germany)
Friday, August 06, 2010, room Hörsaal 2
Maximizing the Kullback-Leibler distance
Nihat Ay proposed the following problem [1], motivated from statistical learning theory: Let be an exponential family. Find the maximizer of the Kullback-Leibler distance
from
. A maximizing probability measure P has a lot of interesting properties. For example, the restriction of
to the support of P will be equal to P, i.e.
if
(for the proof in the most general case see [2]). This simple property can be used to transform the problem into another form. The first observation is that probability measures having this ``projection property'' always come in pairs
, such that
and
have the same sufficient statistics A and disjoint supports. Therefore we can solve the original problem by investigating the kernel of the sufficient statistics
. If we find all local maximizers of
subject to , then we know all maximizers of the original problem. The talk will present the transformed problem and its relation to the original problem. In the end I will give some consequences for the solutions of the original problem.
[1] N. Ay: An Information-Geometric Approach to a Theory of Pragmatic Structuring. The Annals of Probability 30 (2002) 416-436.
[2] F. Matúš: Optimality conditions for maximizers of the information divergence from an exponential family. Kybernetika 43, 731-746.
Date and Location
August 02 - 06, 2010
University of Leipzig
Augustusplatz
04103 Leipzig
Germany
Scientific Organizers
Nihat AyMax Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
Germany
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
Italy
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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
RIKEN
Brain Science Institute, Mathematical Neuroscience Laboratory
Japan
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
Hungary
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
Hungary
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
Italy
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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