## 2 Materials and Methods
### Procedure
#### 2.3.4 Feature Importance Algorithms for Feature Explanation  
Feature importance algorithms were used to select the variables that have a higher impact on the outcome of the models. Feature permutation importance and SHAP summary plots are the two algorithms commonly accepted in the scientific community [38; 39]. Feature permutation importance [39] is based on repeated permutations of the outcome vector to estimate the distribution of measured importance for each variable in a non-informative setting. SHAP assigns each feature an importance value for a particular prediction [40]. SHAP values attribute to each feature the change in the expected model prediction when conditioning on that feature. 3.5 Probabilistic and Statistical Analysis: Values Selection Based on Maximizing the Desired Effectiveness and Minimizing the Undesired One  
Shapley values and its variants are adequate \"local model-agnostic methods\", which provide interesting insights of a single prediction. Global explanation methods can help understand the model through visualizations and explanations of the final model weights [40]. As the aim of the study was to understand how to maximize the serve effectiveness (how and why specific values of the selected features affect the predicted target variables), the goal was to calculate which values threshold of the selected features maximize the likelihood of effectiveness type 1 and minimize the likelihood of effectiveness type 4. For this purpose, a novel semiautomated algorithm based on classical statistics was developed. The first steps of this process were the following:  
* First, a smooth probability distribution of the data using the kernel density estimation algorithm (KDE), together with statistical estimators, was calculated for each selected feature. The estimators were mainly the mean, the MLE, and percentiles 5 and 95 for each type of effectiveness. * Then, the values were mostly identified by selecting the area of the plot which combined a higher density of the points with the desired result (type 1) and a lower density of the undesired result (type 4). The statistical estimators also helped to understand the probability distribution. 3.6 Synthetic Dataset Generation and Simulation Based on the Predictions on the Dataset and Analysis of Improvements in Effectiveness  
In the final step, a synthetic dataset using the selected values was generated, and the prediction was simulated. Since the model reached 93% f1-score, the predictions were reliable, at least for this specific dataset. By doing this, the approach was validated, and values could be adjusted to improve the rate of effectiveness. The next steps in the process were the following:  
* The values outside the desired selected threshold were substituted by random values inside it and, therefore, a synthetic dataset was generated. * Then, predictions on the whole dataset were performed using the deep learning model previously trained. Then, the final rates of Ef1 and Ef4 were calculated. It is important to comment that the synthetic dataset assumes a role in the validation of the explanatory algorithm. Following the application of \"feature importance\" algorithms to identify the most significant variables, an assessment is conducted to determine values that contribute to increased efficiency, relying on insights derived from probability density plots. The values selected are oriented towards maximizing the probability of efficiency 1 within the confines of the real dataset. To validate this optimization, the original dataset undergoes modification, wherein the values of each variable are adjusted in accordance with the proposed recommendations. Specifically, the dataset is 'clipped', entailing the substitution of values outside the established range limits with randomly generated values falling within the recommended limits. Subsequently, the trained model is employed to generate new predictions on this adjusted dataset.