← 研踪 PaperTrailarXiv:2404.07661 · v3
Robust performance metrics for imbalanced classification problems
首次提交 2024-04-11 19:50
版本更新 2026-10-29 15:03
雷达观测 2026-10-30 13:28
摘要
We show that established performance metrics in binary classification, such as Matthews' correlation coefficient (MCC), Cohen's $κ$, the F-score or the Jaccard similarity coefficient are not robust to class imbalance in the sense that if the proportion of the minority class tends to $0$, the true positive rate (TPR) of the Bayes classifier under these metrics {becomes very small or even tends to $0$}. Thus, in imbalanced classification problems, these metrics favour classifiers which ignore the minority class. To alleviate this issue we introduce robustified modifications of the MCC, of Cohen's $κ$ and of the F-score with an additional tuning parameter which allows to adapt the amount of robustness against class imbalance. As theoretical guarantee we show that the Bayes-optimal classifier for these robustified performance metrics, when expressed in terms of the density ratio $f_1/f_0$ of the class-conditional densities $f_i$, has a threshold parameter which is upper-bounded in terms of the tuning parameters. Therefore, even in strongly imbalanced settings, the TPR associated to this classifier will be bounded away from $0${, provided that $f_1/f_0$ exceeds this bound with positive probability under the positive class}. We numerically illustrate the behaviour of the various performance metrics and the effect of the tuning parameters in simulations as well as on a credit default data set. We also discuss connections to the receiver operating characteristic and precision-recall curves, which provide an alternative perspective on the proposed notion of robustness, and give recommendations on how to combine their usage with performance metrics.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v3 · 2026-10-29 15:03 · 最新观测版本
Robust performance metrics for imbalanced classification problems
We show that established performance metrics in binary classification, such as Matthews' correlation coefficient (MCC), Cohen's $κ$, the F-score or the Jaccard similarity coefficient are not robust to class imbalance in the sense that if the proportion of the minority class tends to $0$, the true positive rate (TPR) of the Bayes classifier under these metrics {becomes very small or even tends to $0$}. Thus, in imbalanced classification problems, these metrics favour classifiers which ignore the minority class. To alleviate this issue we introduce robustified modifications of the MCC, of Cohen's $κ$ and of the F-score with an additional tuning parameter which allows to adapt the amount of robustness against class imbalance. As theoretical guarantee we show that the Bayes-optimal classifier for these robustified performance metrics, when expressed in terms of the density ratio $f_1/f_0$ of the class-conditional densities $f_i$, has a threshold parameter which is upper-bounded in terms of the tuning parameters. Therefore, even in strongly imbalanced settings, the TPR associated to this classifier will be bounded away from $0${, provided that $f_1/f_0$ exceeds this bound with positive probability under the positive class}. We numerically illustrate the behaviour of the various performance metrics and the effect of the tuning parameters in simulations as well as on a credit default data set. We also discuss connections to the receiver operating characteristic and precision-recall curves, which provide an alternative perspective on the proposed notion of robustness, and give recommendations on how to combine their usage with performance metrics.
查看此版本解读 →查看此版本原文 ↗