多类边界分类的泛化误差

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摘要翻译：
本文研究了多类边缘分类器泛化误差的收敛速度。特别地，我们发展了一个上限理论来量化各种大裕度分类器的泛化误差。该理论允许处理一般的边缘损失，凸或非凸，存在或不存在一个支配类。建立了三个主要结果。首先，对于任何固定的裕度损失，关于候选决策函数类的选择，在理想的和实际的推广性能之间可能存在一种折衷，这种折衷取决于近似误差和估计误差之间的折衷。实际上，不同的保证金损失导致在具体情况下的理想或实际表现不同。其次，我们证明了在线性学习问题中，收敛速度可以随输入/输出对的联合分布而任意加快。这超出了预期的利率$O(n^{-1}）$。第三，我们建立了几个边缘分类器在特征选择中的收敛速度，允许候选变量的数目$P$大大超过样本量$n$但不超过$\exp(n)$。
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英文标题：
《Generalization error for multi-class margin classification》
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作者：
Xiaotong Shen, Lifeng Wang
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The theory permits a treatment of general margin losses, convex or nonconvex, in presence or absence of a dominating class. Three main results are established. First, for any fixed margin loss, there may be a trade-off between the ideal and actual generalization performances with respect to the choice of the class of candidate decision functions, which is governed by the trade-off between the approximation and estimation errors. In fact, different margin losses lead to different ideal or actual performances in specific cases. Second, we demonstrate, in a problem of linear learning, that the convergence rate can be arbitrarily fast in the sample size $n$ depending on the joint distribution of the input/output pair. This goes beyond the anticipated rate $O(n^{-1})$. Third, we establish rates of convergence of several margin classifiers in feature selection with the number of candidate variables $p$ allowed to greatly exceed the sample size $n$ but no faster than $\exp(n)$.
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PDF链接：
https://arxiv.org/pdf/708.3556

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关键词：distribution Multivariate Convergence classifiers performance generalization rates off 候选 超出