## 3 Results
Figure 3: SHAP summary plot. Figure 4: SHAP dependence plot for “Acuity”. Figure 5: SHAP dependence plot for “Hours”. The reason why we chose to create dependence plots for \"Acuity\", \"Hours\", and \"Age\" is mainly due to their prominence in the summary plot, suggesting they have a high magnitude of impact on the model's predictions. The dependence plots for these features can potentially highlight the relationship between each feature and the target variable, as well as any possible interaction effects between these features and others. In conclusion, our results highlight the power of the Gradient Boosting Machine and SHAP values in providing insightful interpretability of complex models. The SHAP summary plot and dependence plots offered an intuitive understanding of feature importance and their interactions in a way that simple global feature importance methods cannot match. In future work, it would be useful to investigate and compare other feature interpretation methods as well as other model types. The force plot illustrates how each feature is pushing the model output away from the base value (expected value) and towards the output value for that specific instance (row of data). The base value is the average prediction for all instances, and the output value is the prediction for the particular instance we are inspecting. The features that push the prediction higher are shown in red, while the features that push the prediction lower are shown in blue. The force plot (Figure 7) provides a detailed view of how the model makes decisions. By looking at this plot, we can understand how the value of each feature contributes positively or negatively to the final prediction, which further enhances our interpretability of the model's behavior. It represents a single patient's visit to the hospital with a gradient-boosting machine predicting their hospitalization risk. We start with the red values. * \"Hours\" has a SHAP value of 8.217, meaning that the number of hours contributes to increasing the model's prediction compared to the base value. In other words, this feature is pushing the prediction higher. * \"Age\" of 76 years also increases the model's prediction. As per the data, older patients are likely to have a higher risk of requiring hospitalization. * \"Arrival transport WALK IN\" with a value of 0 also contributes to increasing the risk, suggesting that patients arriving by other means than walking in might be more unwell, and therefore at a higher risk of hospitalization. * \"Acuity\" with a value of 2 also contributes to an increase in the model's prediction. Higher acuity might mean a more serious condition, and hence a higher hospitalization risk. Figure 6: SHAP dependence plot for “Age”. Next, we interpret the blue values:  
\"Heartrate\" with a value of 68 contributes to decreasing the model's prediction. A lower heart rate might be indicative of a stable condition, hence lowering the risk of hospitalization. \"SBP\" (systolic blood pressure) with a value of 145, also lowers the model's prediction. High systolic blood pressure might indicate a patient's body's response to a health stressor, but in the context of other parameters, this is lowering the predicted risk in the model. \"Temperature\" of 97.9 degrees Fahrenheit also decreases the model's prediction, as it is close to the average body temperature, indicating no sign of fever, hence lowering the hospitalization risk. The SHAP force plot for a single patient visit provides insightful explanations at an individual level. The red features (i.e., \"Hours\", \"Age\", \"Arrival transport WALK IN\", \"Acuity\") drive the model's prediction higher compared to the base value, while the blue features (i.e., \"Heartrate\", \"SBP\", \"Temperature\") pull it lower. For instance, a longer time since the last assessment (8.217 h) and older age (76 years old) are notable factors increasing the predicted risk of hospitalization. The transport method upon arrival and a higher acuity level also contribute to this increased risk.