什么是 Bayes error rate

最新推荐文章于 2025-01-12 20:26:58 发布

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最新推荐文章于 2025-01-12 20:26:58 发布

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原文链接：http://www.cnblogs.com/bennyblue/p/9091440.html

本文探讨了统计分类中贝叶斯错误率的概念及其重要性。贝叶斯错误率是随机结果分类中最低可能的错误率，相当于不可约简误差。文章介绍了几种估算贝叶斯错误率的方法，并讨论了其在模式识别与机器学习领域的应用。

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In statistical classification, 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.^[1]^[2]

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.^[2]

The Bayes error rate finds important use in the study of patterns and machine learning techniques.^[3]

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:^{[citation needed]}

$p=1-\textstyle \sum _{C_{i}\neq C_{\text{max,x}}}\int \limits _{x\in H_{i}}P(C_{i}|x)p(x)\,dx$

where x is an instance, C_i is a class into which an instance is classified, H_i is the area/region that a classifier function h classifies as C_i.^{[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]}

转载于:https://www.cnblogs.com/bennyblue/p/9091440.html