## 4 Experiments
### Approach Application to Two Real-Life Use Cases
#### 4.2.2 Use Case on Crime in Communities  
**Dataset and Settings. ** The Crime and Communities dataset contains 1994 records of communities described by socio-economic and demographic factors, including their crime rates [18]. In particular, the dataset involves 128 numerical variables, related to, e.g., average income, average household size, percentages of different ethnic groups, percentages of people at different degree of education and percentage of people using public transport. We preprocessed the dataset by performing common data cleaning tasks; namely, we removed variables involving missing values, as well as variables involving a single value, since they would have only led to noise in the analysis. The cleaned dataset involved 91 attributes. We applied supervised discretization to convert numerical variables into categorical; more precisely, we used the default settings of the supervised discretization technique implemented in Weka ([[https://www.cs.waikato.ac.nz/ml/weka/](https://www.cs.waikato.ac.nz/ml/weka/)]([https://www.cs.waikato.ac.nz/ml/weka/](https://www.cs.waikato.ac.nz/ml/weka/)), Last access 16 March 2022), which strives to determine the most discriminative intervals with respect to the class. Figure 9: Zoom on the first models containing Personal status (**a**) and Foreign worker (**b**) in the experiment with support 0.09 and confidence 0.9. As in [19], we selected variable ViolentCrimePerPop as the class attribute, where values lower than 20 represent the _positive_ decision and values equal to or greater than 20 represent the _negative_ decision. Among the four values of the variable racePctBlack, the sensitive item is: racePctBlack \(=[0.375,1]\). Accordingly, the decisional process is considered to be affected by discrimination if the fact that black people are the majority in the community has influenced the final decision. **Results. ** Table 8 reports the descriptive statistics for the 80 experiment runs for varying levels of support (\([0.03,0.10]\) with steps of 0.01) and confidence (\([0.5,0.95]\) with steps of 0.5). The number of models, while being consistently lower than the number of rules, is significantly higher those we obtained in the German dataset, approximately in the same order of magnitude as the number of rules. The number of regressors, on the other hand, shows a reduction in more than ten times with respect to the number of rules (models), along with a smaller standard deviation (and, therefore, a more stable output). The median obtained for rules and models in this experiment setting produces 1693 and 1565, respectively, while the median value for the regressors is 167. Moreover, we observe a maximum of 210 regressors to consider (as opposed to, respectively, 6355 rules and 3593 models). Figure 10 reports the relation between regressors and rules across experiments. We observe a trend similar to the one we observed for the German dataset, i.e., a strong variability in the rule mining results for different support and confidence settings, despite relatively stable regressor outputs. Furthermore, in this case, the number of rules exceeds the number of regressors of a factor ranging from 10 to 1000, depending on the support level. A notable exception, however, can be seen in the experiments with support higher than 0.8 and maximum confidence. This is due to the fact that, in these cases, only a few rules were mined, with the result that the output of rule mining is in this case comparable with that obtained using our approach. In one case, for the configuration with the highest threshold, only one rule was mined, from which nine significant regressors were extracted. Figure 11 reports the (log) ratio between regressors and rules for each experiment setting. These results are consistent with what we observed for both the synthetic and German datasets: especially for low levels of these settings, there is a strong reduction in the candidates in the result set.