About: On the Relation between Generalized Entropy and the Bayes Decision Error

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We deal with the relation between generalized entropies (f-entropies) of a discrete random variable and the minimal posterior probability of error (Bayes error) when the value of the random variable is estimated. The tightness of their relation is studied by the means of recently introduced measure called the average inaccuracy. This measure is defined as a standardized average difference between the upper and the lower bound for the Bayes error under given entropy. It can be applied to any strictly concave f-entropy and used to evaluate its relation to the Bayes error. However, due to a complex form of the formula of the average inaccuracy, it is difficult to compare the average inaccuracies of most f-entropies analytically. We propose a smooth approximation of the lower bound for the Bayes error under given f-entropy that simplifies the formula. We show that under this approximation, the quadratic entropy has the tightest relation to the Bayes error among f-entropies. We deal with the relation between generalized entropies (f-entropies) of a discrete random variable and the minimal posterior probability of error (Bayes error) when the value of the random variable is estimated. The tightness of their relation is studied by the means of recently introduced measure called the average inaccuracy. This measure is defined as a standardized average difference between the upper and the lower bound for the Bayes error under given entropy. It can be applied to any strictly concave f-entropy and used to evaluate its relation to the Bayes error. However, due to a complex form of the formula of the average inaccuracy, it is difficult to compare the average inaccuracies of most f-entropies analytically. We propose a smooth approximation of the lower bound for the Bayes error under given f-entropy that simplifies the formula. We show that under this approximation, the quadratic entropy has the tightest relation to the Bayes error among f-entropies. (en)
Title	On the Relation between Generalized Entropy and the Bayes Decision Error On the Relation between Generalized Entropy and the Bayes Decision Error (en)
skos:prefLabel	On the Relation between Generalized Entropy and the Bayes Decision Error On the Relation between Generalized Entropy and the Bayes Decision Error (en)
skos:notation	RIV/67985807:_____/10:00351622!RIV11-MSM-67985807
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M06014), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Horáček, Martin
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 informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	276909
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/10:00351622
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	generalized entropy; f-entropy; Bayes error; average inaccuracy; power entropy; quadratic entropy; Shannon’s entropy; Emlen’s index; Ferreri’s index; Good’s index (en)
http://linked.open.../riv/klicoveSlovo	quadratic entropy Bayes error Emlen’s index Ferreri’s index Good’s index Shannon’s entropy average inaccuracy f-entropy generalized entropy power entropy
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[31FD80C9E958]
http://linked.open...i/riv/nazevZdroje	European Journal for Biomedical Informatics
http://linked.open...in/vavai/riv/obor	BB
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Centre of Biomedical Informatics
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	6
http://linked.open...iv/tvurceVysledku	Horáček, Martin
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	1801-5603
number of pages	5 (xsd:int)

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