# A Grey-Box Ensemble Model Exploiting Black-Box Accuracy and White-Box Intrinsic Interpretability
## 7 Discussion
### Discussion about the Interpretability of the Grey-Box Model  
The proposed Grey-Box model falls into the intrinsic interpretability category as its output predictor is a White-Box model and by nature all White-Box models are interpretable. Nevertheless, it does not have the disadvantage of low accuracy inherent to methods of this category as it performs as good as post-hoc methods.  
Also, in order to present how the interpretability and explainability of our Grey-Box model comes up in practice, we conducted a case study (experiment example) for the Coimbra dataset utilizing Grey-Box (SMO-RT) because this model exhibited better overall performance. For this task, we made predictions for two instances (persons) utilizing our trained Grey-Box model and now we attempt to explain, in understandable to every human terms, why our model made these predictions. Table 3 presents the values of each attribute for two instances of the Coimbra dataset while a detailed description of the attributes can be found in [24].  
Figure 15 presents the trained Grey-Box model's inner structure. From the interpretation of the Grey-Box model, we conclude that the model suggests as the most significant feature, the \"age\", since it is in the root of the tree, while we can also observe that a wide range of features are not utilized at all from the model's inner structure.  
Furthermore, by observing the inner structure of the model we can easily extract the model predictions for both instances by just following the nodes and the arrows of the tree, based on the feature values of each person, this procedure is performed, until we reach a leaf of the tree which has the output prediction of the model. More specifically, the Instance1 has \"Age \(=51\)\" and for the first node the statement \"age \(\leq 37\)\" is \"false\", thus we move right to the next node which has the statement \"HOMA \(\leq 2.36\)\". This is \"true\", so we move left to \"glucose \(\leq 91.5\)\" which is \"false\" since the Instance1 has \"glucose \(=103\)\". Therefore, the model's prediction for the Instance1 is \"patient\". By a similar procedure we can extract the model's prediction for Instance2 which is \"healthy\". Next, we can also draw some rules from the model and translate them into explanations such as  
* Rule 1: \"The persons which are of age over 37, have HOMA lower than 2.36, and have glucose over than 91.5, most probably are patients\".
* Rule 2: \"The persons which are of age lower than 37 and have glucose lower than 91.5 most probably are healthy.\"  
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & **Age** & **BMI** & **Glucose** & **Insulin** & **HOMA** & **Leptin** & **Adiponectin** & **Resistin** & **MCP-1** & **Class** \\ \hline Instance1 & 51 & 22.892 & 103 & 2.74 & 0.696 & 8.016 & 9.349 & 11.554 & 359.232 & Patient \\ Instance2 & 36 & 28.570 & 86 & 4.34 & 0.920 & 15.12 & 8.600 & 9.150 & 534.22 & Healthy \\ \hline \hline \end{tabular}
\end{table}
Table 3: Feature values for two persons from the Coimbra dataset.  
and so on. Instance1 falls exactly on Rule 1, while Instance2 falls exactly on Rule 2. Thus, an explanation for the Grey-Box model's predictions could be that Instance1 is probably \"patient\" because he/she is older than 37 years old and has very low HOMA with high glucose level, while Instance2 is probably \"_healthy_\" because he/she is under 37 years old and has low glucose level.