## 2 Methodology
### Models Evaluation  
Models' accuracy and interpretability are two important steps for a deeper understanding and assessment of the proposed models.  
Concerning the models' comparison and accuracy measurement, three distinct metrics were calculated [44]: Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Coefficient of correlation (R\({}^{2}\)). On a perfect model, the first two metrics (MAE and RMSE) should present a value close to zero and R\({}^{2}\) equal to one. Although similar, MAE and RMSE allow a model's assessment under distinct and complementary perspectives. When compared with MAE, RMSE penalizes more heavily a model that in a few cases produces high errors since it uses the square of the distance between the real and predicted values [26; 31]. In addition, the Regression Error Characteristic (REC) curve proposed by [PERSON] and [PERSON] [45] was also adopted. An REC curve plots the error tolerance on the \(x\)-axis versus the percentage of points predicted within the tolerance on the \(y\)-axis, allowing quick and easy comparison of different regression models.  
Generalization capacity is also a key point for the model's assessment. For this purpose, in this work, a 5-run under cross-validation (k-fold = 10) approach [44] was implemented. A k-fold validation evaluates the data across the entire training set, but it does so by dividing the training set into \(k\) folds (or subsections, where \(k\) is a positive integer) and then training the model \(k\) times, each time leaving a different fold out of the training data and using it instead as a validation set. In the end, the performance metric is averaged across all \(k\) tests. Lastly, as before, once the best parameter combination has been found, the model is retrained on the full data.  
From an engineering point of view, the model's interpretability is a key aspect to take into account. Due to the high complexity of most ML algorithms, namely SVMs or ANNs that rely on complex statistical analysis and are frequently referred to as \"black boxes\", it is  
Figure 1: Definitions and hyperparameter adopted for each ML algorithm.  
fundamental to find a way to \"open\" such models in order to understand what was learnt by them. With this purpose, [PERSON] and [PERSON] [46] proposed a novel visualization approach based on sensitivity analysis (SA), which is used in this work. SA is a simple method that is applied after the training phase and measures the model responses when a given input is changed, allowing the quantification of the relative importance of each attribute as well as its average effect on the target variable. In particular, it was applied the Global Sensitivity Analysis (GSA) method [46], which is able to detect interactions among input variables. This is achieved by performing a simultaneous variation of \(F\) inputs. Each input is varied through its range with \(L\) levels and the remaining inputs fixed to a given baseline value. In this work, the average input variable value as a baseline was adopted and set to \(L=12\), which allows an interesting detail level under a reasonable amount of computational effort.  
With the sensitivity response of the GSA, different visualization techniques can be computed. In this work, it is calculated the input importance barplot, which shows the relative influence (\(R_{a}\)) of each input variable in the model (from 0 to 100%). The rationale of GSA is that the higher the changes produced in the output, the more important is the input. To measure this effect, first, the gradient metric (\(g_{a}\)) for all inputs was calculated. After that, the relative influence was computed according to the following equation:  
\[R_{a}=\
icefrac{{g_{a}}}{{\sum_{i=1,\delta\text{:}}^{L}\text{:}100(\%)}}\quad \text{where},\quad g_{a}=\sum_{j=2}^{L}\bigl{|}\
icefrac{{g_{a,j}}}{{g_{a,j-1} }}\bigr{|}/(L-1), \tag{1}\]  
where \(a\) denotes the input variable under analysis, and \(\hat{g}_{a,j}\) is the sensitivity response for \(x_{a,j}\).