About: Optimality conditions for maximizers of the information divergence from an exponential family

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The information divergence of a probability measure P from an exponential family E over a finite set is defined as infimum of the divergences of P from Q over Q in E. All directional derivatives of the divergence from E are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for P to be a maximizer of the divergence from E are presented, including new ones when P is not projectable to E. The information divergence of a probability measure P from an exponential family E over a finite set is defined as infimum of the divergences of P from Q over Q in E. All directional derivatives of the divergence from E are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for P to be a maximizer of the divergence from E are presented, including new ones when P is not projectable to E. (en) Informační divergence pravděpodobnostní měry P od exponenciální rodiny E se definuje jako infimum informačních divergencí P od Q cez Q v E. Pro diskrétní E byly explicitně nalezeny všechny směrové derivace informační divergence of E. Za tím účelem bylo studováno chování konjugované funkce k log-Laplacově transformaci. Byly nalezeny všechny podmínky optimality prvního řádu. (cs)
Title	Optimality conditions for maximizers of the information divergence from an exponential family Optimality conditions for maximizers of the information divergence from an exponential family (en) Podmínky oprimality pro informační divergenci od exponenciální rodiny (cs)
skos:prefLabel	Optimality conditions for maximizers of the information divergence from an exponential family Optimality conditions for maximizers of the information divergence from an exponential family (en) Podmínky oprimality pro informační divergenci od exponenciální rodiny (cs)
skos:notation	RIV/67985556:_____/07:00098126!RIV08-AV0-67985556
http://linked.open.../vavai/riv/strany	731;746
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100750603), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Matúš, František
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
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	439760
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/07:00098126
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Kullback-Leibler divergence; relative entropy; exponential family; information projection; log-Laplace transform; cumulant generating function; directional derivatives; convex functions; first order optimality conditions; polytopes (en)
http://linked.open.../riv/klicoveSlovo	polytopes Kullback-Leibler divergence convex functions directional derivatives information projection exponential family relative entropy first order optimality conditions cumulant generating function log-Laplace transform
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[9C8E70597938]
http://linked.open...i/riv/nazevZdroje	Kybernetika
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.
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	43
http://linked.open...iv/tvurceVysledku	Matúš, František
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	0023-5954
number of pages	16 (xsd:int)

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