论文标题
拒绝选项和对KNN的申请的回归
Regression with reject option and application to kNN
论文作者
论文摘要
我们调查了允许戒除预测的回归问题。我们将此框架称为带有拒绝选项的回归，是用拒绝选项的分类扩展。在这种情况下，我们专注于固定拒绝率并得出依赖于条件差异函数阈值的最佳规则的情况。我们提供了涉及两个数据集的最佳规则的半监督估计步骤：使用第一个标记的数据集来估计回归函数和条件差异功能，而第二个未标记的数据集则利用第二个未标记的数据集来校准所需的拒绝率。根据拒绝选项的结果预测变量几乎与在风险和拒绝率方面都具有拒绝期权的最佳预测指标一样好。我们还将我们的方法与KNN算法应用，并在轻度条件下为所得的KNN预测器建立收敛速率。最后，进行了数值研究，以说明使用建议的程序的好处。
We investigate the problem of regression where one is allowed to abstain from predicting. We refer to this framework as regression with reject option as an extension of classification with reject option. In this context, we focus on the case where the rejection rate is fixed and derive the optimal rule which relies on thresholding the conditional variance function. We provide a semi-supervised estimation procedure of the optimal rule involving two datasets: a first labeled dataset is used to estimate both regression function and conditional variance function while a second unlabeled dataset is exploited to calibrate the desired rejection rate. The resulting predictor with reject option is shown to be almost as good as the optimal predictor with reject option both in terms of risk and rejection rate. We additionally apply our methodology with kNN algorithm and establish rates of convergence for the resulting kNN predictor under mild conditions. Finally, a numerical study is performed to illustrate the benefit of using the proposed procedure.
