## 5 Discussion  
### Feature Importance Analysis  
Feature importance analysis can be used to explain the predictions of machine learning models and provides a deeper understanding, helping to comprehend the importance of features in the model, enhancing its interpretability and trustworthiness. SHAP (SHapley Additive exPlanations) is a method for explaining machine learning model predictions based on the concept of cooperative game theory [57]. It is used to analyze the impact of each feature on the model's predictions. The main idea behind SHAP feature importance analysis is to explain the model's output based on the contributions of each feature, and the allocation of contributions is influenced by the interactions between features. The SHAP values take into account the impact of a feature on the model output when combined with other features, providing a fair way to allocate the contribution of each feature to the model predictions. For each sample and each feature, SHAP values can explain how much influence that feature has on the prediction output for that sample [58]. A positive value indicates an increase in the predicted value, while a negative value indicates a decrease. The SHAP feature importance estimates for a random forest regression model obtained through Bayesian optimization with gradient boosting trees are shown in Figure 18.  
From Figure 18, it can be observed that the SHAP importance of data related to POI, such as shopping centers, hospitals, schools, companies, government institutions, as well as data on life services, building heights, median nighttime lighting, and artificial land surface in land cover, all rank in the top ten for the random forest regression model's feature importance. This indicates that these mentioned features play an important role in revealing spatial population distribution. Among these, POI data holds a particularly high percentage, and these points of interest are closely related to people's daily lives. As urban development progresses, people's daily life needs are increasing, and the development of services, daily activities, and residential areas is closely tied to the spatial distribution of the population. Therefore, the distribution of geographic points of interest largely determines the spatial distribution of the population. Regarding building height data, with each grid having the same area size, the pixel values representing building heights determine the volume capacity of buildings, reflecting their ability to accommodate people per unit area. Places where the building capacity is larger tend to have larger populations, so building height is a good indicator of population distribution. Nighttime light data reflects human economic activity during the night. Economically developed areas usually host larger populations, which also proves the ability of nighttime light data to indicate population distribution. Human-made surface of land cover represents surfaces formed through human activities, including various human settlements, industrial areas, transportation facilities, etc. These are closely tied to human activities and tend to better reflect human population than other types of land cover. As urban development progresses, the need for daily life amenities increases, and the construction of life services is closely related to the spatial distribution of population. In Sichuan Province, the administrative units consistently influence the distribution of urban centers. Therefore, the shopping centers and administrative institutions in geographic POI to some extent determine the spatial distribution of the population. However, features like water bodies, grassland and forest of land cover, elevation and slope features of terrain, and railway density and road density features of geographic basic information exhibit the lowest importance in modeling. This shows that these factors have weak ability to indicate population information in Sichuan Province. Although Sichuan Province has complex topography, its natural geographical variations are quite distinct.