**4. Discussion**

#### *4.1. Analyses of E*ff*ects of Input Features on Adsorption Isotherms*

#### 4.1.1. Relative Importance of Input Features

Once the estimation model has been constructed, it should be of practical meaning to quantify the e ffect of each input feature on the adsorption isotherm. In this section, the relative importance of each input variable is quantified while using the mean decrease impurity importance (MDI) [52,53]. A most significant advantage of the MDI over conventional Pearson or Spearman coe fficients is that the MDI does not require a priory assumption of linear or monotonic dependence of the output on the input features, which, therefore, should be more accurate in quantifying the e ffects of each input feature [54]. Figure 10 shows that fixed carbon and ash are three key factors that control the adsorption amount. The equilibrium moisture has a relative importance of ≈8.8%, while the remaining factors (temperature, vitrinite, vitrinite reflectance, and inherent moisture) have relative importance of less than 3.0%, which suggests the very minor or even negligible influences of these factors on the adsorption amount. Here, it is noted the e ffect of vitrinite reflectance is significantly diluted when compared with the correlation analysis in Section 2.3, which is possibly due to the collinearity between the vitrinite reflectance and fixed carbon for the coal samples (Figure 11). The existence of collinearity may result in the abnormal response of the output to one or several of the collinear inputs [55]. Fixed carbon demonstrates an obviously stronger correlation on the adsorption capacity than vitrinite reflectance does and, thus, the e ffect of the vitrinite reflectance has a high risk of being overridden by the fixed carbon considering their collinearity, as can be seen from Figure 4b,c.
