## 4 Results
### AD Definition during ML Model Construction (Substudy 2)  
#### 4.2.1 Dimensionality Reduction on the Preprocessed Data without Outliers  
To improve the interpretability of the models, a dimensionality reduction step based on GA is applied on the preprocessed data after outlier elimination through Layout 3. Note that the GA algorithm enables us to remove _descriptors_ that are not relevant for the predicted property, while the elimination of X-outliers removes _molecules_ that exhibit outlier behavior based on their descriptor values. The obtained performances are presented in Tables 3 and 4 for the enthalpy and entropy, respectively, where configurations with or without outliers/dimensionality reduction are compared. The removal of the outliers enables us to improve the performance of the models (configurations A vs. B, and C vs. D), although the resulting AD might be restricted due to the elimination of some molecules. The dimensionality reduction does not seem to have a major impact on the performance (configurations A vs. C, and B vs. D), despite the significant reduction in the number of descriptors that are reduced from more than 2000 to only 100, thus enhancing the subsequent interpretability of the models. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Property** & **Outliers** & **Mol.** & **Desc.** & \(\mathbf{R^{2}}\) & \(\mathbf{R^{2}}\) & \(\mathbf{MAE}\) & \(\mathbf{MAE}\) & \(\mathbf{RMSE}\) & \(\mathbf{RMSE}\) \\  & **Elimination** & & & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline \multirow{2}{*}{H} & Layout 3, with y-outliers & 1531 & 2506 & 0.998 & 0.995 & 9.51 & 11.88 & 12.72 & 19.41 \\  & Layout 3, without y-outliers & 1525 & 2506 & 0.998 & 0.996 & 9.39 & 11.69 & 12.61 & 17.56 \\ \hline \multirow{2}{*}{S} & Layout 3, with y-outliers & 1514 & 2479 & 0.996 & 0.995 & 7.49 & 8.19 & 9.90 & 11.40 \\  & Layout 3, without y-outliers & 1431 & 2479 & 0.991 & 0.988 & 7.56 & 8.28 & 10.00 & 11.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the performance of the models in absence and in presence of y-outliers. \(MAE\) and \(RMSE\) are in kJ/mol and J/mol/K for the **enthalpy** and the **entropy**, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Configuration** & **Outlier** & **Dimensionality** & **Mol.** & **Desc.** & \(\mathbf{R^{2}}\) & \(\mathbf{R^{2}}\) & \(MAE\) & \(MAE\) & \(RMSE\) & \(RMSE\) \\  & **Elimination** & **Reduction** & & & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline A & No & No & 1785 & 2506 & 0.997 & 0.978 & 16.08 & 26.96 & 30.90 & 71.76 \\ \hline B & Yes & No & 1531 & 2506 & 0.998 & 0.995 & 9.51 & 11.88 & 12.72 & 19.41 \\ \hline C & No & Yes & 1785 & 100 & 0.995 & 0.978 & 15.45 & 24.16 & 36.90 & 70.77 \\ \hline D & Yes & Yes & 1531 & 100 & 0.998 & 0.994 & 9.27 & 11.89 & 14.09 & 21.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Effects of outlier elimination (Layout 3) and dimensionality reduction (GA) on the model performance in predicting **enthalpy** (J/mol). In particular, for the enthalpy, with or without outlier elimination (configurations C and D), the 100 identified descriptors mostly belong to the following categories as defined by AlvaDesc: 2D atom pairs, atom-centered fragments and atom-type e-state indices. For the entropy, the most represented categories in the 100 identified descriptors, that seem to also depend on the outlier elimination step, are the following: 2D atom pairs, 2D autocorrelations and atom-centered fragments (instead of 2D atom pairs, functional group counts and CATS 3D descriptors when outliers are not eliminated). Note that the identified descriptors are fully detailed in the Supplementary Materials, as well as their corresponding coefficients in Lasso linear model. To better understand this variation for the entropy, Table A3 displays the most represented families in the eliminated outliers via Layout 3 for both enthalpy and entropy.