Robust performance metrics for imbalanced classification problems

Abstract:We show that established performance metrics in binary classification, such as Matthews' correlation coefficient (MCC), Cohen's $\kappa$, 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 tends to $0$ as well. 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 $\kappa$ 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 $0$. 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.

Machine Learning (stat.ML); Machine Learning (cs.LG); Methodology (stat.ME)

arXiv:2404.07661 [stat.ML]

(or arXiv:2404.07661v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2404.07661 Focus to learn more arXiv-issued DOI via DataCite

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