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In statistical classification, the Bayes error rate is the lowest possible error rate for any classifier of a random outcome (into, for example, one of two categories) and is analogous to the irreducible error.〔Fukunaga, Keinosuke (1990) ''Introduction to Statistical Pattern Recognition'' by ISBN 0122698517 pages 3 and 97〕〔K. Tumer, K. (1996) "Estimating the Bayes error rate through classifier combining" in ''Proceedings of the 13th International Conference on Pattern Recognition'', Volume 2, 695–699〕 A number of approaches to the estimation of the Bayes error rate exist. One method seeks to obtain analytical bounds which are inherently dependent on distribution parameters, and hence difficult to estimate. Another approach focuses on class densities, while yet another method combines and compares various classifiers.〔 The Bayes error rate finds important use in the study of patterns and machine learning techniques. ==Error determination== In terms of machine learning and pattern classification, the labels of a set of random observations can be divided into 2 or more classes. Each observation is called an ''instance'' and the class it belongs to is the ''label''. The Bayes error rate of the data distribution is the probability an instance is misclassified by a classifier that knows the true class probabilities given the predictors. For a multiclass classifier, the Bayes error rate may be calculated as follows: : where ''x'' is an instance, ''Ci'' is a class into which an instance is classified, ''Hi'' is the area/region that a classifier function ''h'' classifies as ''Ci''. The Bayes error is non-zero if the classification labels are not deterministic, i.e., there is a non-zero probability of a given instance belonging to more than one class. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bayes error rate」の詳細全文を読む スポンサード リンク
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