. "Hor\u00E1\u010Dek, Martin" . . "1"^^ . "RIV/67985807:_____/10:00351622" . . "1"^^ . "On the Relation between Generalized Entropy and the Bayes Decision Error" . . "RIV/67985807:_____/10:00351622!RIV11-MSM-67985807" . "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 . . . . "276909" . "generalized entropy; f-entropy; Bayes error; average inaccuracy; power entropy; quadratic entropy; Shannon\u2019s entropy; Emlen\u2019s index; Ferreri\u2019s index; Good\u2019s index"@en . "[31FD80C9E958]" . . . . . "5"^^ . . "On the Relation between Generalized Entropy and the Bayes Decision Error" . . "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." . "P(1M06014), Z(AV0Z10300504)" . . . "1801-5603" . . . "On the Relation between Generalized Entropy and the Bayes Decision Error"@en . . . "6" . . . . "On the Relation between Generalized Entropy and the Bayes Decision Error"@en . . "CZ - \u010Cesk\u00E1 republika" . . "1" . "European Journal for Biomedical Informatics" .