## 2 Materials and Methods
### Supervised Machine Learning Models and Performance Metrics  
In this paper, we employed different linear and nonlinear supervised ML-based models for identifying if a patient has performed PA. In particular, we used four state-of-the-art models, including DT, logistic regression (LR), K-nearest neighbors (KNN), and support vector machine (SVM). We selected these ML models based on different factors, including ease of implementation, extensive use in benchmarking studies, and because they have been used and internationally validated in multiple clinical studies, reaching great performance. Additionally, aiming to improve the predictive performance, we considered two ensemble models RF and the extreme gradient boosting (XGB), the neural network-based model named multilayer perceptron (MLP), and a novel predictive transformer-based model for tabular data named TabPFN. LR is a linear model used for classification that uses a logistic function that finds the best fitting coefficients to describe the relationship between the independent variables (input features) and the dependent variable (target/label vector) [42]. Once the LR model is trained, it can be used to predict the probability of a sample belonging to a positive class based on its input variables. A common threshold is set at 0.5, where probabilities above the threshold are classified as positive, and those below are classified as negative. KNN is a nonlinear model that classifies an unlabeled sample according to the class that is most frequent within its \(K\)-nearest neighbors [43]. First, these neighbors are found by a similarity measure (e.g., Euclidean distance), and then the unlabeled sample is assigned the class that is most frequent within its K-nearest neighbors. KNN mainly depends on two hyperparameters: the similarity measure and the number of neighbors \(K\). The former is used to measure how similar a sample is from others, being the Euclidean distance one of the most used. The latter is representative of the neighborhood size. Choosing an adequate value of \(K\) is highly related to predictive performance, with larger values generating more complex model decision boundaries and smaller values creating simpler ones [43]. SVM is a model that allows both linear and nonlinear approximations [44]. SVM aims to find an optimal hyperplane in a high-dimensional space (called feature space) that separates the samples into a discrete number of predefined classes. This hyperplane determines the margin between the classes, and when data are not linearly separable, different kernel functions (e.g., polynomial, radial basis, sigmoid) can be used to maximize margins between hyperplanes [45]. RF is a model that generates an ensemble of simpler models, particularly training multiple DTs [46]. Each DT is trained using a subsample of the training set, and then, a combination of the DTs are used to make the final predictions. This approach with different samples and models helps to reduce overfitting and improve generalization. MLP is a type of artificial neural network and it consists of an input layer, various hidden layers, and an output layer, where each neuron in each layer is fully connected to neurons in the subsequent layers. MLP uses nonlinear activation functions to learn complex patterns and relationships from data, and the back-propagation algorithm is used to update the weights of the connections by aiming to minimize errors. TabPFN is a transformer-based model specifically designed for supervised classification on tabular datasets [47]. It combines a transformer architecture called prior-data fitted network (PFN) [47] and Bayesian inference to solve classification tasks over tabular data. TabPFN does not require training from scratch on new data, and presents excellent classification results and low computational complexity. XGB is an algorithm based on a gradient boosting tree that employs an ensemble approach to integrate several weak models and improve model predictions.