A simple method for combining estimates to improve the overall error rates in classification
A simple method for combining estimates to improve the overall error rates in classification
复制标题
一种组合估计以提高分类总体错误率的简单方法
DOI：
10.1007/s00180-015-0571-0
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发表时间：
2015
影响因子：
1.3
通讯作者：
M. Mojirsheibani
中科院分区：
文献类型：
--
作者：
N. Balakrishnan;M. Mojirsheibani
我们提出了一种新的且易于实现的程序，用于组合 J≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J\ge 2$$\end{document} 不同的分类器，以便开发更有效的分类规则。该方法的工作原理是找到新观察（必须分类）的类条件期望的非参数估计，以 J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} 向量为条件\setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} 对应于 J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} 的预测值\setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} 单个分类器。在这里，我们提出了一种数据分割方法来进行各种类别条件期望的估计。事实证明，在相当小的假设下，所提出的组合分类器是最优的，因为其总体误分类错误率渐近小于（或等于）任何一个单独分类器的误分类错误率。还进行了模拟研究来评估所提出的方法。此外，为了使数值结果更具挑战性，我们还考虑具有相当高维度的稳定分布（柯西）。
We present a new and easy-to-implement procedure for combining J≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J\ge 2$$\end{document} different classifiers in order to develop more effective classification rules. The method works by finding nonparametric estimates of the class conditional expectation of a new observation (that has to be classified), conditional on the vector of J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} predicted values corresponding to the J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} individual classifiers. Here, we propose a data-splitting method to carry out the estimation of various class conditional expectations. It turns out that, under rather minimal assumptions, the proposed combined classifier is optimal in the sense that its overall misclassification error rate is asymptotically less than (or equal to) that of any one of the individual classifiers. Simulation studies are also carried out to evaluate the proposed method. Furthermore, to make the numerical results more challenging, we also consider stable distributions (Cauchy) with rather high dimensions.