# 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  
In Scenario _S1--complete data debiasing_, our results showed that the sanitization improves prediction of the decision. In addition to possible explanations (e.g., drop of diversity, the similarity between profiles), it suggests that the sanitization transforms the data such that all of the attributes-values are aligned with both the attribute distribution and the conditional distributions obtained by combining attributes. As an illustrative example, consider a dataset in which the profiles are composed of a binary sensitive attribute _gender_ with values \(S_{0}\) and \(S_{1}\), an attribute _occupation_ and other attributes \(X\) which are identical for all profiles. Moreover, we assume that 80% of profiles in the group \(S_{0}\) have the value _Adm-cleral_ for _occupation_, while the rest of the profiles have the value \(Craft\)-_repair_. From this example, we can see that a classifier would predict the _occupation_ attribute without difficulties if the attribute _gender_ is included as the _occupation_ is strongly correlated with the group membership. The sanitization process applied on this data would update the conditional distribution of _occupation_ (since other attributes have identical values) by taking into account the predictability of the sensitive attribute (which should be reduced) and also aligning the value of attribute _occupation_ with the distributions of other attributes. Thus, to prevent the inference of the sensitive attribute, the _occupation_ values would be modified such that \(Pr(S_{0}|occupation)=Pr(S_{1}|occupation)\), while the alignment of the value would ensure that \(Pr(X|occupation,S_{0})=Pr(X|occupation,S_{1})\). The _occupation_ would therefore be modified such that members of both groups \(S_{0}\) and \(S_{1}\) have the same decision. A similar, but more complex process could occur during the sanitization of data with higher and more complex distributions. From this observation, if the decision attribute is strongly correlated with the sensitive attribute, the sanitization process would not necessarily result in a huge decrease of the accuracy in predicting the decision accuracy, even though the damage on the decision is  
Figure 13: Accuracy of decision prediction on Adult dataset. With the proportion, the value oscillates between the minimum corresponding to the original data (86.25), and the maximum obtained using the complete sanitized set (96%). The standard deviation is below 0.012.  
significant. In other words, the sanitization transforms the data by removing correlations with the sensitive attribute, while correcting (based on the given data distributions) some distributions mismatch (as explained in our illustrative example) based on both the sensitive attribute and the characteristics of the dataset. The sanitization protocol does not take into account the semantic meaning of potential attribute-value combinations, but rather the alignment of conditional distributions. To go one step further in our investigations, we considered the attribute _relationship_ of the dataset _Adult_ as the decision attribute, which is correlated with the sensitive attribute _gender_. In Table 6, we present the distribution of the attribute _relationship_ as well as the conditional distributions in the dataset. We observed that the value _Husband_, which is predominant in the dataset, represents only the _Male_ group. The _Female_ group, is mostly identified with the values _Wife_ and _Unmarried_, which represents almost 15.2% of the dataset. In addition, the attributes _Own-child_ and _Not-in-family_ are most present in the _Female_ group. Attributes _relationship_ and _gender_ are therefore correlated. We trained the Gradient Boosting (GB) classifier to predict the _relationship_ attribute, which achieves an accuracy of 74.67% on the original data. We observed that the precision and recall are especially high for the value _husband_, but are not significant for other values.