## 4 Experiments
### Approach Validation
#### 4.1.3 Results
\begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline  & **Metric** & **Min** & **1 st Q** & **Mean** & **Median** & **3 rd Q** & **Max** & **sd** \\ \hline \multirow{4}{*}{**Event**} & N\_rules & 0 & 0 & 12.87 & 4 & 13.25 & 139 & 23.74 \\  & Exact & 0 & 0 & 1.01 & 1 & 2 & 3 & 1.15 \\  & Too general & 0 & 0 & 1.77 & 0 & 3 & 7 & 2.38 \\  & Too specific & 0 & 0 & 3.52 & 0 & 2 & 64 & 9.99 \\  & Partial & 0 & 0 & 6.58 & 0 & 5 & 121 & 14.24 \\  & Off target & 0 & 0 & 0.00 & 0 & 0 & 0 & 0.00 \\ \hline \multirow{4}{*}{**Event**} & N\_models\_tot & 0 & 0 & 4.98 & 4 & 8 & 16 & 4.72 \\  & N\_models\_sel & 0 & 0 & 1.05 & 1 & 2 & 6 & 1.11 \\  & Exact & 0 & 0 & 0.35 & 0 & 1 & 5 & 0.65 \\  & Too general & 0 & 0 & 0.53 & 0 & 1 & 6 & 1.03 \\  & Too specific & 0 & 0 & 0.18 & 0 & 0 & 2 & 0.39 \\  & Partial & 0 & 0 & 0.00 & 0 & 0 & 0 & 0.00 \\  & Off target & 0 & 0 & 0.00 & 0 & 0 & 0 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Min, max, mean, median, first and third quantile of the number of rules (first group of rows) and models (second group of rows) obtained in each experiment. Results are arranged in a matrix, where each box represents a set of experiments with varying confidence and support levels (on the \(y\) and \(x\) axis, respectively, values are reported as percentages); the four columns correspond to the four combinations of noise and overlap, whereas the three rows correspond to the number of discriminated groups in the dataset. Recall that overlap does not impact the results when a single discriminated group is considered. The difference in the recommendations obtained for this dataset are mostly due to randomness in the data generation process. We reported them anyway for the sake of completeness. Within each box, each square corresponds to a combination of support and confidence thresholds. Squares are colored on the basis of the density of useful recommendations for the given combination of support and confidence. A darker color indicates a higher density (and vice versa). Blue cells represent support-confidence combinations from which no significant rules/regressors were obtained (resulting in a denominator of zero), and white cells represent support-confidence combinations for which no _exact_ or _too general_ recommendations were obtained. We observe that, across almost all experimental setups, our approach produces a much higher density of relevant recommendations compared to rule mining alone. This confirms the observations made from Table 5; namely, rule mining tends to return a high number of recommendations, in which useful recommendations are hidden among the others. Our approach, instead, provides almost only useful recommendations in almost all performed experiments, with the exception of the experiments involving two and three discriminated groups with no noise and no overlap (first column of the second and third sets of experiments). While this might seem counter intuitive, delving into the corresponding dataset, we find that the over-imposed constraints for data generation turned out to produce unrealistic relations that significantly reduce the discriminating effects of the chosen variables. For more than one discriminated group, and in the absence of noise and overlap, the variable values used for the discriminated groups only occur for subjects fitting the related context. For example, in the experiments with two discriminated groups, we have discriminating context groups, \"SpeakLanguage =Y\" and \"PreviousRole =Employee\". Because of the generation constraints, there are no subjects assuming both these values. This creates the rather unrealistic situation whereby the value of one variable precludes another variable to assume some values. Our approach (correctly) detects a strong correlation among context variables SpeakLanguage and PreviousRole. This leads to the generation of _too specific_ recommendations for most of the support-confidence thresholds, with some exceptions mostly due to the randomness of data.