On the Relation between Generalized Entropy and the Bayes Decision Error

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F10%3A00351622" target="_blank" >RIV/67985807:_____/10:00351622 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the Relation between Generalized Entropy and the Bayes Decision Error

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the Relation between Generalized Entropy and the Bayes Decision Error

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

<a href="/cs/project/1M06014" target="_blank" >1M06014: Centrum biomedicínské informatiky (CBI)</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

European Journal for Biomedical Informatics

ISSN

1801-5603

e-ISSN

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Svazek periodika

6

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

5

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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