标题： 分类的 p 值 显示英文标题

标题： P-values for classification

摘要： 设 $(X,Y)$ 是一个随机变量，由一个观测到的特征向量$X\in \mathcal{X}$和一个未知联合分布的未观测类别标签$Y\in \{1,2,...,L\}$组成。此外，设$\mathcal{D}$为一个训练数据集，它由$n$个完全可观测的独立副本$(X,Y)$构成。 通常的分类程序提供点预测器（分类器） $\widehat{Y}(X,\mathcal{D})$的$Y$或估计$Y$在给定$X$条件下的分布。 为了量化分类$X$的确定性，我们提议为每个$\theta =1,2,...,L$构造一个p值$\pi_{\theta}(X,\mathcal{D})$来检验零假设$Y=\theta$，暂时将$Y$视为固定参数。 换句话说，点预测器$\widehat{Y}(X,\mathcal{D})$被替换为一个具有特定置信水平的$Y$预测区域。 我们认为（i）这种方法优于传统方法，以及（ii）任何合理的分类器都可以被修改以生成非参数p值。 我们讨论了诸如最优性、单次使用和多次使用的有效性，以及计算和图形方面的问题。 显示英文摘要

摘要： Let $(X,Y)$ be a random variable consisting of an observed feature vector $X\in \mathcal{X}$ and an unobserved class label $Y\in \{1,2,...,L\}$ with unknown joint distribution. In addition, let $\mathcal{D}$ be a training data set consisting of $n$ completely observed independent copies of $(X,Y)$. Usual classification procedures provide point predictors (classifiers) $\widehat{Y}(X,\mathcal{D})$ of $Y$ or estimate the conditional distribution of $Y$ given $X$. In order to quantify the certainty of classifying $X$ we propose to construct for each $\theta =1,2,...,L$ a p-value $\pi_{\theta}(X,\mathcal{D})$ for the null hypothesis that $Y=\theta$, treating $Y$ temporarily as a fixed parameter. In other words, the point predictor $\widehat{Y}(X,\mathcal{D})$ is replaced with a prediction region for $Y$ with a certain confidence. We argue that (i) this approach is advantageous over traditional approaches and (ii) any reasonable classifier can be modified to yield nonparametric p-values. We discuss issues such as optimality, single use and multiple use validity, as well as computational and graphical aspects.