# 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
Unexpectedly, the sanitization process did not modify the decision attribute but instead modified the attribute \(note_{1}\) such that the _decision_ attribute is a result of a function applied on other attributes, as well as the similarity of their conditional distributions as we expected (Figure 15). We can also observe that the original \(note_{1}\) does not follow the same distribution as its sanitized counterpart. As a consequence, it would be difficult to train a classifier on one version to predict the other. \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 \(Pr(Y=Y_{x})\) & 59.24 & 21.85 & 18.89 & 0.00 & 0.00 & 0.0044 \\ \(Pr(Y=Y_{x}|S=Male)\) & 61.05 & 21.23 & 17.70 & 0.00 & 0.00 & 0.0033 \\ \(Pr(Y=Y_{x}|S=Female)\) & 55.48 & 23.13 & 21.37 & 0.00 & 0.00 & 0.0068 \\ \(Pr(S=Male|Y=Y_{x})\) & 69.56 & 65.59 & 63.24 & 0.00 & 0.00 & 0.50 \\ \(Pr(S=Female|Y=Y_{x})\) & 30.43 & 34.40 & 36.75 & 0.00 & 0.00 & 0.50 \\ \(Recall_{GB}:Pr(\hat{Y}=Y_{x}|Y=Y_{x})\) & 99.89 & 97.43 & 94.43 & 0.00 & 0.00 & 0.00 \\ \(Precis_{GB}:Pr(Y=Y_{x}|\hat{Y}=Y_{x})\) & 99.97 & 95.09 & 97.02 & 0.00 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sanitized distributions of the attribute _relationship_. Gradient Boosting (GB) Recall (\(Recall_{GB}\)) and Precision (\(Precis_{GB}\)) when predicting the relationship values. Note that the classifier is trained without the sensitive attribute. Numerical values are given in percentage. On a similar synthetic dataset in which we have augmented the discrimination (the threshold is increased for group \(gender=0\) and decreased for the other), we obtained similar observations about the _alignment_. In addition, attribute \(note_{3}\) is rendered nearly identical for both groups (Figure 16). The state of \(note_{3}\) is due to either the prevention of inference or the improper reconstruction which has not been completed yet. Figure 14: Distribution of all attributes in the datasets. Top: Original data distribution, Bottom: Sanitized distributions. From left to right, attributes: \(note_{1}\), 2, 3 and the decision. The original data shows the similarity between distributions, but different decisions. The sanitizer aligned the distribution of \(note_{1}\) such that it match the decision criteria, the sensitive attribute has not been hidden yet. Figure 15: Decision boundary based on the mean of all attributes \(note_{x}\) on original (left-most) and sanitized (second left) for the group \(gender=0\) (top) and \(gender=1\) (bottom). The sanitization has modified the decision boundary of both groups, such that they are almost identical. The modification is only on attribute \(note_{1}\), which means that the decision attribute is not affected. \(Orig\) denotes the original distribution while \(San\) refers to the sanitized one. The sanitized distribution of \(note_{1}\) thus matches the decision boundary. When pushed further on this dataset, the sanitization process triples the protection, by modifying all attributes such that the sensitive attribute is protected. The overall similarity of distributions is preserved while the deviation is reduced as shown in Figure 17.  
We believe that the alignment due to the sanitization explains the discordance between the sanitized decisions and the original ones.