A note on margin-based loss functions in classification
A note on margin-based loss functions in classification
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DOI：
10.1016/j.spl.2004.03.002
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发表时间：
2004-06-01
影响因子：
0.8
通讯作者：
Lin, Y
中科院分区：
文献类型：
--
作者：
Lin, Y
在许多分类过程中，分类函数是通过最小化训练样本上的某个经验风险来获得的。然后基于分类函数的符号进行分类。近年来，已经提出了许多使用不同的基于边缘的损失函数的分类方法。基于边缘的损失函数通常被激励为误分类损失的上界，但这不能解释分类过程的统计特性。我们发现，一个大家庭的利润为基础的损失函数是Fisher一致的分类。也就是说，损失函数的总体最小化导致贝叶斯最优分类规则。我们的结果涵盖了几乎所有的边际损失函数，已在文献中提出。我们给出了一个不等式，将基于保证金的损失函数的Fisher一致性与基于这些损失函数的方法的一致性联系起来。我们利用这个不等式得到了基于一类边际损失函数的筛法的收敛速度。(C)2004 Elsevier B.V.保留所有权利。
In many classification procedures, the classification function is obtained by minimizing a certain empirical risk on the training sample. The classification is then based on the sign of the classification function. In recent years, there have been a host of classification methods proposed that use different margin-based loss functions. The margin-based loss functions are often motivated as upper bounds of the misclassification loss, but this cannot explain the statistical properties of the classification procedures. We show that a large family of margin-based loss functions are Fisher consistent for classification. That is, the population minimizer of the loss function leads to the Bayes optimal rule of classification. Our result covers almost all margin-based loss functions that have been proposed in the literature. We give an inequality that links the Fisher consistency of margin-based loss functions with the consistency of methods based on these loss functions. We use this inequality to obtain the rate of convergence for the method of sieves based on a class of margin-based loss functions. (C) 2004 Elsevier B.V. All rights reserved.