Divergence from factorizable distributions and matroid representations by partitions

0333424 - ÚTIA 2010 RIV US eng J - Journal Article
Matúš, František
Divergence from factorizable distributions and matroid representations by partitions.
[Divergence faktorizačních distribucí a matroidy reprezentované parciálností.]
IEEE Transactions on Information Theory. Roč. 55, č. 12 (2009), s. 5375-5381. ISSN 0018-9448. E-ISSN 1557-9654
R&D Projects: GA AV ČR IAA100750603; GA ČR GA201/04/0393
Institutional research plan: CEZ:AV0Z10750506
Keywords : Information divergence * relative entropy * Shannon entropy * exponential family * hierarchical model * log-linear model * contingency table * Gibbs distribution * matroid representation * secret sharing scheme * maximum likelihood.
Subject RIV: BA - General Mathematics
Impact factor: 2.357, year: 2009
http://library.utia.cas.cz/separaty/2009/MTR/matus-divergence from factorizable distributions and matroid representations by partitions.pdf

Maximization of the information divergence from any hierarchical log-linear model is studied. A new upper bound on the maximum is presented and its tightness analyzed. For the models given by the bases of a matroid, the latter is related to matroid representations by partitions or, equivalently, to ideal secret sharing schemes. A new link between the divergence maximization, the maximum likelihood principle and secret sharing is established.

Byla studována maximalizace informační divergence od hierarchických log-lineárních modelů. Byl nalezen nový odhad na maximum a diskutována jeho těsnost. Ta je v úzké souvislosti s reprezentacemi matroidů rozklady. Výsledky umožňují novou interpretaci ideálních schemat sdílení tajemství v kryptografii pomocí principu maximální věrohodnosti.
Permanent Link: http://hdl.handle.net/11104/0178409