Correction: Popoola, G.; Sheppard, J. Investigating and Mitigating the Performance–Fairness Tradeoff via Protected-Category Sampling. Electronics 2024, 13, 3024

In the original publication [1], there were mistakes in Section 2, where the false negative rate should be corrected to the false positive rate. A correction has been made to the third sentence of Paragraph 4 in Section 2.

The revised sentence is as follows:

EOD states that a binary classifier $\widehat{y}$ is fair if its False Positive Rate (FPR) and True Positive Rate (TPR) are equal across the domain of $\mathcal{S}$ [21].

The following equation has also been revised in Section 2.

Original equation:

$$EOD=TP{R}_n\left(\widehat{y}\right)-FP{R}_n\left(\widehat{y}\right)$$

Corrected equation:

$$EOD=\underset{i\ne j}{\max }\left\{\right|TP{R}_i\left(\widehat{y}\right)-TP{R}_j\left(\widehat{y}\right)|, |FP{R}_i\left(\widehat{y}\right)-FP{R}_j\left(\widehat{y}\right)\left|\right\}.$$

Additionally, due to the incompleteness of the published version, which does not provide the full mathematical definition of statistical parity, two equations have been added for completeness to end of Section 2. The revised version is as follows:

$$P\left(\widehat{y}=1|S=w\right)=P\left(\widehat{y}=1|S=n\right)$$

Similar to EOD, this can be extended to multiple classes such that

$$P\left(\widehat{y}=1|S=i\right)=P\left(\widehat{y}=1|S=j\right), \forall i\ne j.$$

From this, SP can be calculated similarly to EOD by considering the pairwise differences across the protected categories.

$$SP=\underset{i\ne j}{\max }\left\{\right|P(\widehat{y}=1|S=i)-P(\widehat{y}=1|S=j)| \}.$$