## 4 Experimental Results
### Cross-Validation Experiments
Finally, the rules extracted from the decision stumps provided the highest average fidelity (99.9%) and the lowest complexity (5.4 rules with 2.0 antecedents). \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Model** & **Acc.** & **Fid.** & **Acc. R. (a)** & **Acc. R. (b)** & **Nb. R.** & **Nb. Ant.** \\ \hline DIMLP (25) & **93.4** (0.5) & 96.3 (0.8) & 92.1 (0.8) & 94.4 (0.4) & 18.5 (0.6) & 2.9 (0.0) \\ DIMLP (50) & 93.0 (0.6) & 95.8 (0.8) & **92.3** (1.1) & **94.5** (0.6) & 18.3 (0.6) & 2.9 (0.1) \\ DIMLP (100) & 93.0 (0.6) & 95.9 (0.7) & 92.1 (0.7) & 94.4 (0.5) & 18.8 (0.7) & 2.9 (0.0) \\ DIMLP (150) & 93.1 (0.7) & 96.1 (0.9) & 91.6 (0.8) & 94.1 (0.6) & 18.2 (0.8) & 2.9 (0.0) \\ \hline RF (25) & 93.2 (0.7) & 95.7 (1.0) & 91.5 (0.8) & 94.3 (0.6) & 30.2 (1.2) & 3.6 (0.1) \\ RF (50) & **93.4** (0.5) & 95.2 (1.6) & 91.3 (1.4) & **94.5** (0.5) & 32.6 (1.4) & 3.8 (0.2) \\ RF (100) & 93.2 (0.4) & 95.3 (1.0) & 91.5 (1.3) & 94.4 (0.6) & 33.2 (1.2) & 4.0 (0.1) \\ RF (150) & **93.4** (0.4) & 95.9 (1.3) & 91.7 (1.1) & 94.4 (0.4) & 32.2 (0.7) & 4.0 (0.1) \\ \hline RF-3 (25) & 91.9 (0.5) & 97.2 (0.5) & 91.6 (1.0) & 93.0 (0.5) & 13.7 (0.6) & 2.8 (0.1) \\ RF-3 (50) & 92.5 (0.8) & 97.2 (0.7) & 91.6 (0.7) & 93.3 (0.4) & 13.9 (0.4) & 2.8 (0.0) \\ RF-3 (100) & 92.9 (0.7) & 96.5 (0.9) & 91.8 (0.8) & 93.9 (0.8) & 14.2 (0.6) & 2.8 (0.1) \\ RF-3 (150) & 92.9 (0.4) & 96.8 (0.9) & 91.6 (0.9) & 93.6 (0.5) & 14.5 (0.7) & 2.8 (0.1) \\ \hline GB (1,25) & 90.2 (0.4) & **99.6** (0.3) & 90.0 (0.5) & 90.3 (0.5) & **6.5** (0.4) & **1.9** (0.1) \\ GB (1,50) & 92.2 (0.7) & 98.6 (0.6) & 91.9 (0.8) & 92.6 (0.7) & 12.0 (0.3) & 2.5 (0.0) \\ GB (1,100) & 92.8 (0.6) & 98.2 (0.6) & 92.0 (1.0) & 93.2 (0.7) & 14.7 (0.5) & 2.7 (0.1) \\ GB (1,150) & 92.5 (0.7) & 97.4 (0.9) & 91.7 (1.2) & 93.2 (0.9) & 17.1 (0.3) & 2.9 (0.0) \\ \hline GB (2,25) & 91.7 (0.4) & 99.0 (0.6) & 91.4 (0.5) & 92.0 (0.4) & 11.4 (0.5) & 2.5 (0.0) \\ GB (2,50) & 92.3 (0.6) & 97.9 (0.9) & 91.6 (0.8) & 92.9 (0.6) & 17.4 (0.6) & 2.9 (0.1) \\ GB (2,100) & 93.0 (0.4) & 96.6 (1.0) & 91.3 (1.1) & 93.6 (0.8) & 21.4 (1.0) & 3.2 (0.1) \\ GB (2,150) & 93.2 (0.5) & 96.3 (0.8) & 91.3 (0.8) & 93.9 (0.5) & 24.8 (0.9) & 3.4 (0.1) \\ \hline GB (3,25) & 91.6 (0.6) & 97.3 (0.7) & 91.4 (0.8) & 92.6 (0.5) & 16.9 (0.9) & 2.7 (0.1) \\ GB (3,50) & 92.6 (0.5) & 97.0 (1.1) & 91.5 (0.8) & 93.3 (0.4) & 22.6 (0.7) & 3.1 (0.1) \\ GB (3,100) & 92.8 (1.0) & 96.5 (1.0) & 91.0 (1.1) & 93.4 (0.9) & 29.5 (1.2) & 3.5 (0.2) \\ GB (3,150) & 93.0 (0.7) & 95.8 (1.4) & 91.5 (1.4) & 94.1 (0.6) & 33.4 (0.8) & 4.0 (0.1) \\ \hline SR (25) & — & — & 88.4 (0.8) & — & 14.1 (0.9) & 3.0 (0.0) \\ SR (50) & — & — & 87.2 (0.7) & — & 23.1 (0.9) & 3.0 (0.0) \\ SR (100) & — & — & 86.8 (1.5) & — & 40.9 (1.3) & 3.0 (0.0) \\ SR (150) & — & — & 85.6 (0.6) & — & 54.5 (2.1) & 3.0 (0.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average results obtained on the “Ionosphere” dataset. For each column, the highest average accuracy or average fidelity is represented in bold, along with the lowest average number of rules or average number of antecedents. Table 8 illustrates the results for the \"Students-on-Math\" prediction problem. The highest average predictive accuracy was provided by the DIMLP ensembles (92.2%). Again, the most complex rulesets were provided by RFs, on average. With decision stumps trained by GB, we obtained the highest average fidelity (100%) with the simplest extracted rulesets (two rules, on average). Finally, it is worth noting that the rulesets with an average predictive accuracy of 91.8% generated from the DIMLPs had 18.5 rules, on average.