Bayesian Error Rate
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two categories) and is analogous to the irreducible error.[1][2] A number of approaches to the estimation of the Bayes error rate exist. One method seeks to obtain
Bayes Rate Error
analytical bounds which are inherently dependent on distribution parameters, and hence difficult to bayesian error estimation estimate. Another approach focuses on class densities, while yet another method combines and compares various classifiers.[2] The Bayes error
Bayes Error Rate In R
rate finds important use in the study of patterns and machine learning techniques.[3] Error determination[edit] In terms of machine learning and pattern classification, the labels of a set of random observations can bayes error rate example 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:[citation needed] optimal bayes error rate p = ∫ x ∈ H i ∑ C i ≠ C max,x P ( C i | x ) p ( x ) d x {\displaystyle p=\textstyle \int \limits _{x\in H_{i}}\sum _{C_{i}\neq C_{\text{max,x}}}P(C_{i}|x)p(x)\,dx} 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.[clarification needed] 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.[citation needed] See also[edit] Naive Bayes classifier References[edit] ^ Fukunaga, Keinosuke (1990) Introduction to Statistical Pattern Recognition by ISBN 0122698517 pages 3 and 97 ^ a b 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 ^ Hastie, Trevor. The Elements of Statistical Learning (2nd ed.). http://statweb.stanford.edu/~tibs/ElemStatLearn/: Springer. p.17. ISBN978-0387848570. This statistics-related article is a stub. You can help Wikipedia by expanding it. v t e Retrieved from "https://en.wikipedia.org/w/index.php?title=Bayes_error_rate&oldid=732668070" Categories: Statistical classificationBayesian statisticsStatistics stubsHidden categories: All articles with unsourced statementsArticles with unsourced statements f
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