Fast learning rates for plug-in classifiers
Fast learning rates for plug-in classifiers
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DOI：
10.1214/009053606000001217
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发表时间：
2007-04-01
影响因子：
4.5
通讯作者：
Tsybakov, Alexandre B.
中科院分区：
文献类型：
--
作者：
Audibert, Jean-Yves;Tsybakov, Alexandre B.
最近已经表明，在裕度（或低噪声）假设下，存在获得超额贝叶斯风险的快速收敛速率的分类器，即，比n（-1/2）更快的速率。关于这一主题的工作提出了以下两个假设：（i）最佳可实现的快速速率是n（-1）阶，以及（ii）插件分类器通常比基于经验风险最小化的分类器收敛得更慢。我们表明，这两种假设都是不正确的。特别是，我们构建的插件分类器，不仅可以实现快速，而且超快的速度，即速度快于n-1。我们建立极大极小下界表明，所获得的利率不能得到改善。
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than n(-1/2). The work on this subject has suggested the following two conjectures: (i) the best achievable fast rate is of the order n(-1), and (ii) the plug-in classifiers generally converge more slowly than the classifiers based on empirical risk minimization. We show that both conjectures are not correct. In particular, we construct plug-in classifiers that can achieve not only fast, but also super-fast rates, that is, rates faster than n-1. We establish minimax lower bounds showing that the obtained rates cannot be improved.