The subject of this thesis is the maximization of the information divergence from an exponential family on a finite set, a problem first formulated by Nihat Ay. A special case is the maximization of the mutual information or the multiinformation between different parts of a composite system.
My thesis contributes mainly to the mathematical aspects of the optimization problem. A reformulation is found that relates the maximization of the information divergence with the maximization of an entropic quantity, defined on the normal space of the exponential family. This reformulation simplifies calculations in concrete cases and gives theoretical insight about the general problem.
A second emphasis of the thesis is on examples that demonstrate how the theoretical results can be applied in particular cases. Third, my thesis contain first results on the characterization of exponential families with a small maximum value of the information divergence.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-77355 |
| Date | 19 October 2011 |
| Creators | Rauh, Johannes |
| Contributors | Universität Leipzig, Fakultät für Mathematik und Informatik, Priv.-Dz. Nihat Ay, Prof. Dr. Jürgen Jost, Prof. Dr. Jürgen Jost, Prof. Dr. Andreas Knauf |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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