Publication details

Journal Article

Divergence from factorizable distributions and matroid representations by partitions

: IEEE Transactions on Information Theory vol.55, 12 (2009), p. 5375-5381

: CEZ:AV0Z10750506

: IAA100750603, GA AV ČR, GA201/04/0393, GA ČR

: Information divergence, relative entropy, Shannon entropy, exponential family, hierarchical model, log-linear model, contingency table, Gibbs distribution, matroid representation, secret sharing scheme, maximum likelihood.

: 10.1109/TIT.2009.2032806

: http://library.utia.cas.cz/separaty/2009/MTR/matus-divergence from factorizable distributions and matroid representations by partitions.pdf

(eng): 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.

(cze): 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.

: BA