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 formula33 be an exponential family. Find the maximizer of the Kullback-Leibler distance formula35 from formula33. A maximizing probability measure P has a lot of interesting properties. For example, the restriction of formula41 to the support of P will be equal to P, i.e. formula47 if formula49 (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 formula51, such that formula53 and formula55 have the same sufficient statistics A and disjoint supports. Therefore we can solve the original problem by investigating the kernel of the sufficient statistics formula59. If we find all local maximizers of
equation17
subject to formula61, 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 Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
Germany
Contact by Email

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
Contact by Email
Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42