Classification is a fundamental task in many applications on which data-driven methods have shown outstanding performances. However, it is challenging to determine whether such methods have achieved the optimal performance. This is mainly because the best achievable performance is typically unknown and hence, effectively estimating it is of prime importance. In this paper, we consider binary classification problems and we propose an estimator for the false positive rate (FPR) of the Bayes classifier, that is, the optimal classifier with respect to accuracy, from a given dataset. Our method utilizes soft labels, or real-valued labels, which are gaining significant traction thanks to their properties. We thoroughly examine various theoretical properties of our estimator, including its consistency, unbiasedness, rate of convergence, and variance. To enhance the versatility of our estimator beyond soft labels, we also consider noisy labels, which encompass binary labels. For noisy labels, we develop effective FPR estimators by leveraging a denoising technique and the Nadaraya-Watson estimator. Due to the symmetry of the problem, our results can be readily applied to estimate the false negative rate of the Bayes classifier.

本文提出了一种用于估计贝叶斯分类器中的假阳性率的估计器，并对其进行了广泛的理论分析，包括一致性、无偏性、收敛速度和方差。此外，还通过利用去噪技术和Nadaraya-Watson估计器，开发了一种用于估计有噪声标签情况下的假阳性率的有效估计器。由于问题的对称性，我们的结果还能被直接应用于估计贝叶斯分类器的假阴性率。

基于数据驱动的Bayes二元分类器假阳性率估计与软标签