# Fidex and FidexGlo: From Local Explanations to Global Explanations of Deep Models +
## 4 Experiments with Tabular Data
### An Introductory Experiment  
With the \"Iris\" classification problem belonging to three classes, we performed experiments based on ten repetitions of 10-fold cross validation trials. Table 2 illustrates the results, with the standard deviations in brackets. QSVMs were not trained here, as our current implementation is for datasets belonging to two classes. The first row of this table refers to DIMLP architectures without a second hidden layer, the second to DIMLPs with a second hidden layer of ten neurons, the third to RFs of depth ten, the fourth to RFs of unlimited depth, the fifth to GBs of depth one, and the last to GBs of depth three.  
The highest average prediction accuracy of the rules (Acc. R. a) was provided by the DIMLPs with 95.3%. The same model also produced the lowest average number of rules (4.5) and antecedents per rule (1.6). RFs and GBs tended here to generate a higher number of rules. Finally, the average fidelity on the testing sets was over 99% for all models. Figure 3 shows an example of ruleset including four rules generated from a DIMLP ensemble. Incross-validation trials, its accuracy was 96% on the training set and 100% on the testing set. In Figure 4, it is worth presenting a more complex ruleset, generated from a GB with a depth of three and containing ten rules. The prediction accuracy of this second ruleset was 100% on both training and testing sets during cross-validation trials.  
The rules generated by the FidexGlo algorithm are not ordered. In other words, the rules are not linked by an else statement, meaning that one or more rules are activated for each sample. If a sample activates the rules that belong to more than one class, only the rules of the class that is provided by the model are kept, while the others are discarded. The first ruleset, due to its small size, makes it easy to understand how an iris is classified. The second ruleset is longer and more detailed and includes rules covering a small number of samples. It is perhaps more interesting for understanding iris classification in detail.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Acc.** & **Fid.** & **Acc. R. (a)** & **Acc. R. (b)** & **Nb. R.** & **Nb. Ant.** \\ \hline DIMLP (\(h_{2}=0\)) & 94.9 (0.5) & 99.6 (0.5) & **95.3** (0.5) & 95.3 (0.5) & **4.5** (0.4) & **1.6** (0.1) \\ DIMLP (\(h_{2}=10\)) & 94.5 (0.6) & 99.5 (0.5) & 94.5 (0.8) & 94.7 (0.7) & 5.9 (0.6) & 1.9 (0.1) \\ \hline RF (\(d=10\)) & **95.3** (0.5) & 99.5 (0.5) & 94.9 (0.5) & 95.3 (0.5) & 10.5 (0.3) & 2.4 (0.0) \\ RF (—) & 95.2 (0.8) & 99.1 (0.8) & 94.8 (0.5) & 95.4 (0.7) & 10.4 (0.2) & 2.4 (0.0) \\ \hline GB (\(d=1\)) & 94.3 (0.6) & **99.8** (0.3) & 94.2 (0.5) & 94.3 (0.6) & 7.7 (0.4) & 2.3 (0.1) \\ GB (\(d=3\)) & **95.3** (0.4) & 99.5 (0.6) & 95.1 (0.6) & **95.5** (0.4) & 10.3 (0.3) & 2.4 (0.0) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average results obtained on the “Iris” dataset by cross-validation. Bold numbers are the lowest for the last two columns and the highest for the others.  
Figure 3: An example of ruleset generated by FidexGlo applied to an ensemble of 25 DIMLPs with a single hidden layer.