## 4 Experiments
### Approach Validation
#### 4.1.3 Results
We observe a similar though not as strong effect on the experiments with overlap and no noise. The constraint on the noise led to obtain some correlations between some context group values which in turn led to generate some misleading recommendations. Nevertheless, the overall density values remain high. We point out that the presence of such correlations is a by-product of the data generation constraints and is unlikely to represent a realistic situation under real-life conditions. Therefore, we  
Figure 3: Density results for the synthetic dataset. (**a**) density results for models in the synthetic dataset; and (**b**) density results for rules in the synthetic datasets. do not expect this behavior to affect the reliability of the recommendations provided by the approach in real-life contexts. It is worth noting that, while we observe performance to significantly vary for rule mining depending on the support/confidence thresholds, our approach proved to be more stable, keeping a constant level of density in almost all cases. This is in line with previous observations that rule mining is sensitive to parameterization, and that choosing the correct parameter configuration largely depends on unknown structures in the data. By contrast, our approach performs well across the board. This effectively removes the need for fine-tuning the support and confidence thresholds for rule selection, with regression model selection doing the larger part of the heavy lifting required to cherry-pick relevant rules and discarding imprecise ones. **Regressors vs. rules. ** The previous paragraph discussed the results obtained at the regression models level. Here we focus on the obtained regressors. Table 6 shows descriptive statistics about rules and regressors obtained for the tested datasets. The table shows some interesting trends. First, we observe much more variation in the number of rules than in the number of regressors (sd = 23.74 and 1.93, respectively), and that extreme values far away from the median are more likely to appear in the former than in the latter distribution. This confirms that the outcome of our approach is much more stable than the rule mining outcome. Furthermore, it is straightforward to see that, on average, the number of regressors is significantly lower than the number of rules. This is particularly evident from the mean value, equal to 12.87 for the rules, while the mean number of regressors is 2.11, with a six-fold reduction. An even stronger reduction can be observed considering the maximum values (139 for the rules, 6 for the regressors). Figure 4 reports the relation between regressors and rules across the experiments for each dataset. Each grid corresponds to a single experimental setting (i.e., to one combination of support and confidence threshold); the \(x\) axis shows the number of extracted rules, while the \(y\) axis shows the number of extracted regressors. Different symbols and colors are used to represent the complexity of the dataset. A common trend for all datasets is that the number of rules exceeds the number of regressors for at least one order of magnitude at low support/confidence thresholds. Even when increasing the support/confidence thresholds, for most of the tested configurations, the number of rules was at least twice the number of regressors. To visualize the order of magnitude in the difference between regressors and rules, Figure 5 reports (on a log scale) the ratio between regressors and rules for each experimental setting (without considering configurations where no rules were found). We observe that the datasets involving noise are also the ones in which we observe a stronger difference between the number of rules/regressors. In both datasets, we obtained at most the same numbers of regressors and rules, while in most of the configurations, the number of regressors is significantly lower (up to a three-fold reduction compared to the number of rules).