## 3 Materials and Methods
### Validation Method and Algorithms  
We used the 10-fold cross-validation method with five repetitions to validate the ML models MLP, GBM, DT, RF, XGBoost, KNN, SVM, and LR (weak/strong regularization). An MLP is a feedforward neural network, meaning data travels in a single direction [18]. This model comprises one (or more) hidden neurons between the layers related to inputs and outputs.  
In contrast, the GBM is a decision tree with a fixed size that uses a boosting strategy [19]. This algorithm features integrated attribute selection, producing an estimation, approximation, or the function denoted as \(F^{*}(x)\), which maps the input \(x\) to the output \(y\) while minimizing the expected value by using a loss function \(L(y,F(x))\) across the joint distribution [20].  
A DT algorithm commonly applies a divide-and-conquer strategy to construct a directed acyclic graph, where rule splitting is determined by maximizing information gain [21]. DT algorithms such as C4.5 include internal attribute selection, and the information gain is influenced by the concept of entropy, which quantifies the uncertainty or randomness associated with a discrete random variable. DT offers the advantage of straightforward result interpretation by following the decision rules of a single tree [22; 23; 24].  
Similarly, the RF relies on classification and regression tree principles while following specific guidelines for tree growth, combination, self-testing, and post-processing [25]. The algorithm includes an embedded attribute selection mechanism, evaluated using the Gini impurity criterion index. RF also facilitates a straightforward interpretation of results from the individual trees within the ensemble.  
Relying on a different approach, KNN is a distance-based algorithm that classifies new instances using the distance from neighbor instances [26]. Given an instance as a point in space, KNN computes the distance between two points.  
SVM is an algorithm designed to handle binary data using a linear separator to maximize the distance between data points. The algorithm considers concepts such as the separation hyperplane, maximum margin hyperplane, and soft margin [18].  
Lastly, LR extends linear regression, assessing the connections between variables in probabilistic classifications. The algorithm employs a sigmoid function to model these relationships and predict the probability of class membership [27]. Regularization can also be employed to prevent overfitting. We used the LR algorithm as a baseline to compare the linear model with the above ML approaches.  
Moreover, we calculated the mean results for classification metrics, including precision, accuracy, recall, Brier score, Receiver Operating Characteristic Curve (ROC), and Area Under the Precision-Recall (PR) curve. We used the random search method to fine-tune the hyperparameters of the algorithms, aiming to enhance their performance. Furthermore, we analyzed recall-related outcomes using the Friedman and Nemenyi statistical tests to improve the comparisons among the ML models [28]. The Friedman test is a valuable statistical method for identifying differences between models. The Nemenyi test is pertinent for grouping classification models based on assessing differences through many comparisons. We determined the Critical Difference (CD) between the ML models by employing the Nemenyi test, with a significance level set at \(\alpha=0.1\). If the performance differences among models are within an interval more minor than the CD, it suggests that the models are indistinguishable from each other [8].