# Local Data Debiasing for Fairness Based on Generative Adversarial Training
## 5 Experimental Evaluation
### Experimental Results  
_General results on Adult._ Figure 2 describes the achievable trade-off between fairness and fidelity obtained on Adult. First, we can observe that fairness improves when \(\alpha\) increased as expected. Even with \(\alpha=0\) (i.e., maximum utility with no focus on the fairness), we cannot reach a perfect fidelity to the original data as we get at most \(fid_{\alpha=0}\approx 0.982\) (cf. Figure 2). Increasing the value of \(\alpha\) from 0 to a low value such as 0.2 provides a fidelity close to the highest possible (\(fid_{\alpha=0.2}=0.98\)), but leads to a BER that is poor (i.e., not higher than 0.2). Nonetheless, we still have a fairness enhancement, compared to the original data (\(fid_{orig}=1\), \(BER\leq 0.15\)). At the other extreme in which \(\alpha=1\), the data is sanitized without any consideration of the fidelity. In this case, the \(BER\) is optimal as expected and the fidelity is 10% lower than the maximum achievable (\(fid_{\alpha=1}\approx 0.88\)). However, slightly decreasing the value of \(\alpha\), such as setting \(\alpha=0.96\), allows the sanitizer to significantly remove the unwarranted correlations (\(BER\approx 0.45\)) with a cost of 2.24% on fidelity (\(fid_{\alpha=0.96}\approx 0.95\)). With respect to \(sAcc\), the accuracy drops significantly when the value of \(\alpha\) increases (cf. Figure 3). GANSan renders the accuracy of predicting \(S\) from the sanitized set closer to the optimal values, which is the proportion of the privileged group in this case. However, it is nearly impossible to reach that ideal value, even at the extreme sanitization \(\alpha=1\)Similarly to BER, slightly decreasing \(\alpha\) (from 1) by setting \(\alpha=0.85\) improves the sanitization while leading to a fidelity closer to the achievable maximum. The quantitative analysis with respect to the diversity is shown in Figure 4. More precisely, the smallest drop of diversity obtained is 3.57%, which is achieved when we set \(\alpha\leq 0.2\). Among all values of \(\alpha\), the biggest drop observed is 36%. The application of GANSan, therefore introduces an irreversible perturbation as observed with the fidelity. This loss of diversity implies that the sanitization reinforces the similarity between sanitized profiles as \(\alpha\) increases, rendering them almost identical or mapping the input profiles to a small number of stereotypes. When \(\alpha\) is in the range \([0.98,1]\) (i.e., complete sanitization), 75% of categorical attributes have a proportion of modified records between 10% and 40% (cf. Figure 4). Figure 3: Fidelity-fairness trade-off on Adult. Each point represents the minimum possible _sAcc_ of all the external classifiers. _sAcc_ decreases with the increase of \(\alpha\), a small value providing a low fairness guarantee while a larger one usually introduced a higher damage. Remark that even with \(\alpha=0\), a small damage is to be expected. Points whose \(fidelity=1\) (lower right) represent the \(BER\) on the original (i.e., unperturbed) dataset. Figure 2: Fidelity-fairness trade-off on Adult. Each point represents the minimum possible \(BER\) of all the external classifiers. The fairness improves with the increase of \(\alpha\), a small value providing a low fairness guarantee while a high one causes greater damage to the sanitized data. For numerical attributes, we compute the relative change (\(RC\)) normalized by the mean of the original and sanitized values:  
\[RC =\frac{|original-sanitized|}{f(original,sanitized)} \tag{7}\] \[f(original,sanitized) =\frac{|original|+|sanitized|}{2} \tag{8}\]  
We normalize the RC using the mean (since all values are positives) as it allows us to handle situations in which the original values are equal to 0. With the exception of the extreme sanitization (\(\alpha=1\)), at least 70% of records in the dataset have a relative change lower than 0.25 for most of the numerical attributes. Selecting \(\alpha=0.9875\geq 0.98\) leads to 80% of records being modified with a relative change less than 0.5 (cf. Figure A1 in Appendix A).