## 2 Materials and Methods
### Machine Learning Models Validation  
To ensure the robust evaluation of our machine learning models, we implemented a comprehensive validation approach combining 10-fold cross-validation and independent test set assessment. The cross-validation procedure partitions the training data into 10 distinct subsets (k = 10) [22], iteratively training the model on nine subsets while using the remaining subset for validation. This process repeats until each subset is the validation set once, with final performance metrics representing the average across all iterations. While computationally intensive, this approach optimizes data utilization--particularly valuable for limited datasets--while providing reliable performance estimates. The models were further validated on a completely independent test set to confirm generalizability.  
Model performance was evaluated using receiver operating characteristic (ROC) analysis, which quantifies classification outcomes through four metrics: true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN) [23]. We employed multiple evaluation measures:  
* Sensitivity: The true positive rate, indicating the model's capability to identify immunogenic proteins correctly. \[Sensitivity=\frac{TP}{TP+FN}\] (3)
* Specificity: The true negative rate, reflecting accurate detection of non-immunogenic proteins. \[Specificity=\frac{TN}{TN+FP}\] (4)
* Accuracy: The overall classification performance is calculated as the proportion of correct predictions across all samples. \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}\] (5)
* Area Under the ROC Curve (AUC): Ranging from 0.5 (random chance) to 1.0 (perfect discrimination), assessing overall predictive efficacy.
* Matthew's Correlation Coefficient (MCC): A balanced measure particularly valuable for imbalanced datasets, where +1 represents perfect prediction, \(-1\) indicates total disagreement, and 0 suggests random classification. \[MCC=\frac{TP\times TN-FP\times FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}\] (6)  
To assess the robustness of our models and verify that predictions were not artifacts of chance correlations, we employed Y-scrambling (also known as label permutation) [24]. This validation procedure consists of (1) training the model on the original dataset and recording its performance metrics, followed by (2) repeatedly shuffling the target labels while maintaining feature values, then retraining and evaluating the model. A robust model should perform significantly better on the original data than the permuted datasets. If the model maintains comparable performance across scrambled datasets with low variance, this suggests the initial predictions may have resulted from random correlations rather than meaningful relationships in the data.  
To elucidate the contribution of individual features to model performance, we applied two interpretability techniques to our top-performing models. The scikit-learn library implements the first technique, permutation feature importance. Using this technique, one feature's values are shuffled randomly, and the model's score is tracked as it declines. The second method, drop-column feature importance, involves deleting a whole feature column from the dataset, training a new model, and evaluating its performance. The idea behind both approaches is that removing a feature that is not important should not have a significant negative impact on the model's performance. Features showing minimal effects on model performance when altered or excluded are considered less important for the prediction task.