## 4 Results and Discussion
(**a**) illustrates SHAP based feature importance that computed as an average absolute value of SHAP for each feature, producing a standard bar graph of the ten leading features obtained from XGBSVIR method with respect to the data center energy demand target variable. (**b**) illustrates SHAP summary plot of ten leading features obtained from XGBSVFIR method. The higher the SHAP value of a feature, the more effect it has in effectively modeling the specified problem. For example, the system power (sys_power) has the greatest influence on predicting data center energy demand (denenergy. The coloring represents the impact of features on predicting the target variable at high and low effects (high red, low blue). Figure 2: (**a**) SHAP feature importance plot. (**b**) SHAP summary plot. (**a**) illustrates the SHAP feature importance, computed as an average absolute value of SHAP for each feature, producing a standard bar plot of the ten leading features obtained from XGBSVFIR with respect to the data center ambient temperature target variable. The supply_air is the most important feature that has the greatest impact on predicting ambient temperature (maintaining DC operating environment). (**b**) illustrates the SHAP summary plot of ten leading features obtained from the XGBSVFIR method. The higher the SHAP value of a feature, the more important it is for effectively modeling the problem. For example, supply air has the greatest influence on predicting data center ambient temperature (amb_temp), and its effect is represented by two colors: red for a high impact and blue for a lower impact on predicting the target variable. For example, the supply air is an inlet temperature supplied by the cooling system. It allows the data center to maintain an ambient temperature. Exhaust temperature is dissipated temperature from the computing nodes that should be effectively returned to the computer room air conditioning (CRAC) unit while maintaining the data center's ambient temperature and improving equipment efficiencies. Hence, supply_air and exh_temp are the topmost important features at predicting amb_temp while optimizing DC operations. Figure 2a,b below are plots of the top ten most important features for predicting amb_temp over 2000 data samples. Figure 3a,b below show the importance of SHAP features and SHAP summary plots of features in relation to the data center energy demand target variables. Note that these figures are based on 2000 samples taken from the testing sets. The result shows that the main energy consumers in the data center are the computing nodes, which are represented by sys_power, the total power consumption of the calculation nodes in the center. Hence, sys_power is the topmost influential feature at predicting the data center energy demand. Time-based covariates such as quarter, months, and days have a greater impact on data center energy consumption. Furthermore, we present SHAP dependency plots that can provide the necessary information to understand the feature interactions and underlying patterns. The Shapley interaction of features can be computed as below:  
\[\phi_{i,j}=\sum_{s\subseteq\{i,j\}}\frac{|s|!(X-|s|-2)!}{2(X-1)!}\delta_{ij}(s) \tag{7}\]  
The Shapley interaction of a single feature can be computed by subtracting from the model's main feature impact:  
\[\delta_{ij}(s)=\hat{f}_{x}(s\cup\{i,j\})-\hat{f}_{x}(s\cup\{i\})-\hat{f}_{x}(s \cup\{j\})+\hat{f}_{x}(s) \tag{8}\]  
where \(s\) denotes the average value of all coalitions and \(X\) denotes the feature matrix. Figures 4 and 5 depict SHAP feature dependency plots, which show the interactions of features and their impact on predicting the target variable. For example, Figure 4a-d illustrates the interaction between supply_air and exh_temp, exh_temp with covariate month, syst_util with exh_temp, and sysairflow with cpu2_temp. The indexed feature name is positioned on the x-axis, and the Shapley values are positioned on the y-axis. The vertical lines represent the accumulated information density.