We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k-nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(k+lnn)/n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {O} \left( \sqrt{(k + \ln n)/n} \right) $$\end{document} range around an estimate of generalization error for n in-sample examples.

中文翻译：

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k-最近邻分类器的推测正确错误界限

我们引入了推测正确的方法来推导局部分类器的错误界限。使用它，我们证明了 k 最近邻分类器，尽管它们著名的决策边界断裂，但具有 O(k+lnn)/n\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{ wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {O} \ left( \sqrt{(k + \ln n)/n} \right) $$\end{document} 范围围绕 n 个样本示例的泛化误差估计。