具有有界放弃率的二元分类
Binary Classification with Bounded Abstention Rate
摘要：
我们考虑了相对较少研究的\emph{bounded-rate}设置中的二进制分类问题。我们首先获得一个任意的输入标签分布$P_{XY}$的贝叶斯最优分类器的特性。我们的结果推广并提供了\cite{chow1957optimum}首先获得的结果的替代证明，然后在$P_{XY}$的连续性假设下由\citet{denis2015consistency}重新推导。然后，我们提出了一个插件分类器，采用未标记的样本来决定区域的预防和推导出一个上限的标准\emph{Hölder smoothness}和\emph{margin}的假设下，我们的分类器的超额风险。与\citet{denis2015consistency}的插入规则不同，我们构造的分类器以高概率满足约束条件，并且还可以处理经验cdf中的不连续性。我们还推导出证明我们所提出的算法的极大极小近似最优的下界。为了解决插件分类器在高维度的过度复杂性，我们提出了一个计算效率高的算法，建立在凸损失代理人的先前工作，并获得其超额风险的界限在\emph{realizable}的情况下。我们经验比较所提出的算法的性能与一些UCI基准数据集的基线。
英文摘要：
We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution $P_{XY}$. Our result generalizes and provides an alternative proof for the result first obtained by \cite{chow1957optimum}, and then re-derived by \citet{denis2015consistency}, under a continuity assumption on $P_{XY}$. We then propose a plug-in classifier that employs unlabeled samples to decide the region of abstention and derive an upper-bound on the excess risk of our classifier under standard \emph{Hölder smoothness} and \emph{margin} assumptions. Unlike the plug-in rule of \citet{denis2015consistency}, our constructed classifier satisfies the abstention constraint with high probability and can also deal with discontinuities in the empirical cdf. We also derive lower-bounds that demonstrate the minimax near-optimality of our proposed algorithm. To address the excessive complexity of the plug-in classifier in high dimensions, we propose a computationally efficient algorithm that builds upon prior work on convex loss surrogates, and obtain bounds on its excess risk in the \emph{realizable} case. We empirically compare the performance of the proposed algorithm with a baseline on a number of UCI benchmark datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
