About: Infinitely many information inequalities

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	When finite, Shannon entropies of all subvectors of a random vector are considered for the coordinates of an entropic point in Euclidean space. A linear combination of the coordinates gives rise to an unconstrained information inequality if it is nonnegative for all entropic points. With at least four variables no finite set of linear combinations generates all such inequalities. This is proved by constructing explicitly an infinite sequence of new linear information inequalities and a curve in a special geometric position to the half/-spaces defined by the inequalities. The inequalities are constructed recurrently by adhesive pasting of restrictions of polymatroids and the curve ranges in the closure of a set of the entropic points. When finite, Shannon entropies of all subvectors of a random vector are considered for the coordinates of an entropic point in Euclidean space. A linear combination of the coordinates gives rise to an unconstrained information inequality if it is nonnegative for all entropic points. With at least four variables no finite set of linear combinations generates all such inequalities. This is proved by constructing explicitly an infinite sequence of new linear information inequalities and a curve in a special geometric position to the half/-spaces defined by the inequalities. The inequalities are constructed recurrently by adhesive pasting of restrictions of polymatroids and the curve ranges in the closure of a set of the entropic points. (en)
Title	Infinitely many information inequalities Infinitely many information inequalities (en)
skos:prefLabel	Infinitely many information inequalities Infinitely many information inequalities (en)
skos:notation	RIV/67985556:_____/07:00085052!RIV10-AV0-67985556
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/04/0393), P(IAA100750603), Z(AV0Z10750506)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Matúš, František
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	426113
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/07:00085052
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	information inequality; entropy function; matroid; polymatroid; cones (en)
http://linked.open.../riv/klicoveSlovo	cones entropy function polymatroid matroid information inequality
http://linked.open...ontrolniKodProRIV	[1FA757798806]
http://linked.open...v/mistoKonaniAkce	Nice
http://linked.open...i/riv/mistoVydani	Nice
http://linked.open...i/riv/nazevZdroje	Proceedings of ISIT 2007
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Information geomerty of multidimensional models in statistics and artificial intelligence. Conditional independence structures: information-theoretical approach III.
http://linked.open...UplatneniVysledku	2007
http://linked.open...iv/tvurceVysledku	Matúš, František
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2007-06-24 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
number of pages	4 (xsd:int)
http://purl.org/ne...btex#hasPublisher	IEEE
https://schema.org/isbn	978-1-4244-1397-3

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