# Local Data Debiasing for Fairness Based on Generative Adversarial Training
## 5 Experimental Evaluation
### Experimental Results
#### 5.3.2 Decision Prediction Improvement Induced by the Sanitization
The decision accuracy is, respectively, 85.35% and 52.48% in the _Male_ and _Female_ groups. On the sanitized dataset, the accuracies and distributions are also computed and presented in Table 7. The value of attribute _relationship_ are less associated with the _gender_. On the distribution of the attribute conditioned by the sensitive attribute, we observe a more balanced distribution of values in each group. The most discriminative value _Husband_ is more balanced in both groups. We also observe that the values on the conditional distribution of the _gender_ are more specific to each group. Nonetheless, the distribution is close to the dataset distribution of the same attribute (\(Pr(S=Male)=67\) and \(Pr(S=Male)=33\)). From a semantic perspective, at the time the data was collected, having a profile in the _Female_ group associated with the value _Husband_ might not be semantically meaningful, while from the distributional perspective, the sanitizer has aligned the profiles with their most appropriate values. As a consequence the accuracy of predicting the relationship increases from 74.67% to 98.30% (98.28% and 98.34% in, respectively, the _Male_ and _Female_ groups), even though the damage on that attribute is 24.94%. We used the _cosine_ and _Euclidean_ (which is related to the _MSELoss_ in our sanitization objective) distances to verify whether the profiles whose values have been changed to _Husband_ are closer to other profiles in the _Husband_-group, as profiles from the latter group had not had their values changed by the sanitization (up to 99.84%). However, no particular trends were observed. This observation does not exclude the possibility that a higher-dimensional similarity metric might be used by the sanitization process. The damage of almost 25% implies that using the original values as ground truth will cause a drop in the attribute prediction accuracy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Attributes** & \multicolumn{6}{c}{**Relationship**} \\ \hline
**Values** & **Husband** & **Not-in-Family** & **Own-Child** & **Unmarried** & **Wife** & **Other-Relative** \\ \hline \(Pr(Y=Y_{x})\) & 41.27 & 25.87 & 14.65 & 10.58 & 4.62 & 2.98 \\ \(Pr(Y=Y_{x}|S=Male)\) & 61.14 & 20.60 & 12.11 & 3.71 & 0.0033 & 2.42 \\ \(Pr(Y=Y_{x}|S=Female)\) & 0.0068 & 36.82 & 19.93 & 24.85 & 14.22 & 4.15 \\ \(Pr(S=Male|Y=Y_{x})\) & 99.99 & 53.75 & 55.79 & 23.70 & 0.0478 & 54.78 \\ \(Pr(S=Female|Y=Y_{x})\) & 0.0054 & 46.24 & 44.20 & 76.29 & 99.95 & 45.21 \\ \(Recall_{GB}:Pr(\hat{Y}=Y_{x}|\hat{Y}=Y_{x})\) & 98.86 & 79.45 & 60.88 & 32.77 & 17.94 & 1.90 \\ \(Precis_{GB}:Pr(Y=Y_{x}|\hat{Y}=Y_{x})\) & 89.99 & 62.00 & 66.91 & 53.11 To further demonstrate the possibility of alignment, we created a balanced synthetic dataset with the _gender_ (values 0 and 1) as the sensitive attribute. This dataset is composed of three numerical columns (\(note_{1}\), \(note_{2}\) and \(note_{3}\)), each sampled from a Gaussian distribution of \(mean=15\) and deviation \(std=1\). The decision (\(noteDec\)) for each row is generated by taking the mean of the three numerical columns (\(M_{3}\)), and is biased toward the group 0 by applying different thresholds: for group \(gender=1\), a positive decision is obtained if \(M_{3}>=mean\) while for \(gender=0\), the positive decision is obtained if \(M_{3}>=mean+0.7\). On this synthetic dataset, the decision is correlated with the sensitive attribute, while others are kept identical. Our alignment hypothesis states that the decision attribute will be modified such that the decision threshold is identical for both groups, and such that the decision is obtained as a function of the other columns. By having a threshold independent of groups, the sanitized decision is not correlated with the sensitive attribute and having the decision as a function of other columns ensures that the transformation is not just a randomization process with limited distortions. Our observations are presented in Figure 14, on which the sanitized dataset has the same protection (\(BER\)) as the original one.