## 4 Experiments
### Approach Application to Two Real-Life Use Cases
#### 4.2.1 Use Case on Credit Risk
The results discussed to date show the capability of the approach to significantly reduce the space of candidate hypotheses, with respect to classic association rule mining. Exploring these hypotheses to detect the presence of actual biased relations is, at this point, up to the human policy makers. A detailed analysis of the detected regressors would not be possible here, for the sake of space. Nevertheless, in the following, we briefly discuss how regressor coefficients, together with their confidence intervals, can be used to further aid the policy maker in her analysis. To this end, let us consider the configuration with support equal to 0.09 and confidence equal to 0.9. Figure 8 shows the confidence intervals of the corresponding regressors related to the three variables under investigation in our experiments, i.e., Age, Personal status and Foreign worker. The \(y\) axis shows the coefficient values; the blue cross represents the estimated value of the coefficient of one regressor and the blue line corresponds to its 95% confidence interval. The light-blue without crosses lines group regressors belonging to the same models. The number of lines per model depends on the domain of the corresponding variable. Both Age and Personal status have four different values; therefore, here we  
Figure 6: Rules and regressors for each experimental setting. Figure 7: Fraction of obtained models per rule. have three lines for every model corresponding to the values not used for the baseline in the regression. Foreign worker, instead, is a binary value; hence, each single line belongs to a different model. First, we observe that the three variables occur in the result set with different frequencies: we found 10 models containing Age, 79 containing Personal status and 528 containing Foreign worker. By observing the trend of confidence intervals for each variable, one can already spot which candidate hypotheses look more interesting and which ones, instead, could likely be discarded. For instance, all confidence intervals for Age span across both negative and positive values, indicating no clear effect of Age on the outcome variable. This indicates that Age is not a discriminatory factor on its own. It is worth noting that the variable Age occurs in several rules. Therefore, by applying rule mining alone, one might deem this variable to be influential for the decision, although it has actually no statistically significant impact on the output. The situation is different for the other two variables. For the sake of clarity, Figure 9 zooms in on some models for both the variables. For Personal status, we focus on the first three models since we observe a stable trend from the overall figure, which suggests that similar insights can be derived from any group of models. For Foreign worker, instead, while we still observe a similar trend across the models, there seems to be more variability for the first few models; therefore, we decided to focus on the first ten. Figure 9a shows the third line of every model, corresponding to  
Figure 8: Coefficients confidence intervals for the three features under investigation in the experiment (support 0.09 and confidence 0.9). Variable Age can take four values: \([0,30]\), \((30,41]\), \((41,52]\) and \((52,100]\). The baseline value used in the regression model is \((30,41]\). Variable Personal status can take four values: \(male\_single\), \(female\_div\_or\_dep\_or\_mar\), \(male\_div\_or\_sep\) and \(male\_mar\_or\_wid\). The baseline value used in the regression model is \(female\_div\_or\_dep\_or\_mar\). Variable Foreign worker can take two values: \(Y\), \(N\). The baseline value used in the regression model is \(N\). the value male_single which is always above 0. This suggests that this value of Personal status has a significant and positive impact on the decision, even though not a very strong one. This suggests that male, single candidates are significantly more likely to receive a positive risk class than the baseline group, i.e., non-single females.