## 4 Discussion
### Feature Importance  
Feature importance is a key concept in machine learning that helps explain which factors have the biggest impact on a model's predictions. It shows how much each variable contributes to the model's performance and helps researchers understand the relationships within the data. The method for calculating feature importance depends on the model. For example, in tree-based models like XGBoost, it can be measured by how much a feature reduces errors or how often it is used in decision splits. In GP models, importance is assessed by analyzing symbolic equations to see how strongly a feature influences the output. For hybrid models like GP-XGBoost, these methods are combined with techniques like permutation importance or SHAP values, which quantify how much each feature contributes to the predictions. These tools make it easier to rank features, interpret results, and improve the model. The feature importance results in Figure 9 reveal how different soil properties--such as the initial void ratio (\(e_{0}\)), the liquid limit (LL), the plasticity index (PI), and the water content (\(w\))--affect the prediction of the compression index (\(C_{c}\)). The initial void ratio (\(e_{0}\)) stands out as the most important factor, especially in the GP-XGBoost hybrid model, where it has the highest importance score of 0.55. This highlights its critical role in soil compressibility, as it reflects the soil's structure and potential for volume change. The LL and the PI also contribute significantly, particularly in GP-XGBoost and GP models, with importance scores of 0.240 and 0.220. These properties are linked to soil composition and plasticity, making them reliable indicators of compressibility. Interestingly, water content (\(w\)) is moderately important in the hybrid model, with a score of 0.270, showing its effect on soil behavior. MLR assigns less importance to all features, especially the LL and the w, due to its limited ability to handle complex relationships. These results demonstrate how GP-XGBoost combines the strengths of both GP and XGBoost to give a detailed understanding of soil behavior through feature analysis. It is important to note that the dependency between the liquid limit (LL) and the plasticity index (PI) may have influenced the feature importance rankings. Since the PI is derived from the LL and the PL, this relationship introduces collinearity, potentially inflating the importance of these features in the predictive models. Although the GP-XGBoost model is robust against multicollinearity, this dependency could affect the interpretability of the results, and it is acknowledged as a limitation of this study. Feature importance ranking aligns with fundamental geotechnical principles and reflects the critical role of soil composition and structure in compressibility behavior. The LL and the PI are indicators of a soil's clay mineral content and plasticity, which directly affect compressibility. Higher LL values are typically associated with fine-grained soils rich in montmorillonite or kaolinite, which have a greater capacity to absorb water and undergo volume changes under load. The PI reflects the soil's ability to deform plastically, and a higher PI usually correlates with the greater rearrangement of particles during consolidation, resulting in higher \(C_{c}\) values. The strong feature importance of LL and PI in the model suggests that mineralogical composition and interparticle bonding are key mechanisms driving compressibility. The initial void ratio is a fundamental measure of the porosity and packing density of soil particles. Soils with a high \(e_{0}\) have more interparticle voids that make them more susceptible to settlement when subjected to load. The model's emphasis on \(e_{0}\) highlights the significance of soil structure, particularly the arrangement of particles and pore spaces, in controlling the magnitude of primary consolidation.