Bayes Error Rate In R
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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
Bayesian Error Rate
obtain analytical bounds which are inherently dependent on distribution parameters, and hence bayes error rate example difficult to estimate. Another approach focuses on class densities, while yet another method combines and compares various classifiers.[2] The naive bayes classifier error rate Bayes error 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
R Bayes Factor
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
R Bayes Net
calculated as follows:[citation needed] 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: A
their chapter about it here. Last modified: Mar/2004
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