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On the Relation between Generalized Entropy and the Bayes Decision Error
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SYSNO ASEP 0351622 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title On the Relation between Generalized Entropy and the Bayes Decision Error Author(s) Horáček, Martin (UIVT-O) Source Title European Journal for Biomedical Informatics. - : Pulsus Group - ISSN 1801-5603
Roč. 6, č. 1 (2010), s. 38-42Number of pages 5 s. Language eng - English Country CZ - Czech Republic Keywords generalized entropy ; f-entropy ; Bayes error ; average inaccuracy ; power entropy ; quadratic entropy ; Shannon’s entropy ; Emlen’s index ; Ferreri’s index ; Good’s index Subject RIV BB - Applied Statistics, Operational Research R&D Projects 1M06014 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10300504 - UIVT-O (2005-2011) DOI 10.24105/ejbi.2010.06.1.8 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2011
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