On the Relation between Generalized Entropy and the Bayes Decision Error

Result code in 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>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On the Relation between Generalized Entropy and the Bayes Decision Error

Original language 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BB - Applied statistics, operational research

OECD FORD branch

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Project

<a href="/en/project/1M06014" target="_blank" >1M06014: Centre of Biomedical Informatics</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

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

Name of the periodical

European Journal for Biomedical Informatics

ISSN

1801-5603

e-ISSN

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Volume of the periodical

6

Issue of the periodical within the volume

1

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

5

Pages from-to

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UT code for WoS article

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EID of the result in the Scopus database

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