发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了 AdaBoost 的紧泛化界，给出其泛化误差的上界，该上界结合已有结论与新的投票分类器边距泛化界得到，匹配的下界来自已有工作。
AI 中文摘要
本文中，我们证明 AdaBoost 的泛化误差为 $\u0398\left(\tfrac{d\ln(n\gamma^{2}/d)}{n\gamma^2}+\tfrac{\ln(1/\delta)}{n}\right)$，其中 $\u03b3$ 是弱学习器保证的优势，$d$ 是包含弱假设的类的 VC 维，$n$ 是样本量，$\u03b4$ 是置信参数。本文的贡献是给出了上界，匹配的下界来自已有研究。上界的证明结合了已知结论（AdaBoost 输出的投票分类器其投票函数具有零经验 $\u03b3/2$ 边距损失），以及我们所知的一种新的投票分类器边距泛化界。
英文摘要
In this paper we show that the generalization error of AdaBoost is $Θ\big(\tfrac{d\ln(nγ^{2}/d)}{nγ^2}+\tfrac{\ln(1/δ)}{n}\big)$, where $γ$ is the advantage guaranteed by the weak learner, $d$ is the VC-dimension of the class containing the weak hypotheses, $n$ is the sample size, and $δ$ is the confidence parameter. The contribution of this paper is the upper bound; the matching lower bound follows from prior work. The upper bound proof follows by combining the known fact that AdaBoost outputs a voting classifier whose voting function has zero empirical $γ/2$-margin loss with what is, to the best of our knowledge, a new margin-based generalization bound for voting classifiers.
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