## 3 Experimental Results
### Comparison of a Regularized Mixture of Expert Models  
In this section, the performances of different regularized mixture of experts, MoLE-Lasso, MoLE-EN, MoLE-RR, and Mix-PLS, are compared when using different numbers of samples for training. For this purpose, from the total of the 27 batches, 1, 5, 10, 15, and 20 batches were chosen randomly to compose the training dataset for training the MoLE models, while the original test set of six batches was kept fixed for evaluating the performance. The same procedure was repeated 10 times for each experiment, and then the \(R^{2}\) metric was computed for each repetition. The average results for each of the 10 trials are shown in Table 2, for each model and for the different number of batches in the training dataset. \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Values** \\ \hline \# batches train & 25 \\ \# batches test & 6 \\ \# samples per batches train & 13, 17, 22, 16, 17, 19, 26, 18, 19, 17, 16, 20, 14, 13, 16, 18, 20, 21, 23, 17, 16, 18, 23, 20, 19, 18 \\ average samples per batches train & 18 \\ \# samples per batches test & 23, 21, 24, 20, 19, 20 \\ average samples per batches test & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the polymerization dataset. To complement the analysis, the boxplots of \(R^{2}\) between predictions and test data under a different number of batches for acidity and viscosity are presented in Figure 2. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Acidity**} & \multicolumn{6}{c}{**Viscosity**} \\ \cline{2-9}  & **MoLE** & **MoLE** & **MoLE** & **Mix-PLS** & **MoLE** & **MoLE** & **MoLE** & **MoLE** & **Mix-PLS** \\  & **Lasso** & **RR** & **EN** & **mix-PLS** & **Lasso** & **RR** & **EN** & **mix-PLS** \\ \hline
1 batch & **0.484** & 0.345 & 0.365 & 0.325 & 0.614 & 0.463 & **0.760** & 0.385 \\
5 batches & 0.814 & **0.843** & 0.792 & 0.651 & **0.928** & 0.910 & 0.920 & 0.772 \\
10 batches & **0.910** & 0.883 & 0.891 & 0.817 & **0.930** & 0.920 & 0.924 & 0.821 \\
15 batches & **0.924** & 0.909 & **0.924** & 0.905 & **0.944** & 0.925 & 0.943 & 0.905 \\
20 batches & 0.927 & 0.914 & **0.928** & 0.924 & 0.945 & 0.923 & 0.941 & **0.949** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average \(R^{2}\) values of different regularized MoLE models trained with different numbers of batches on acidity and viscosity datasets. The bold marked values indicate the best performance. Figure 2: Boxplot for the different MoLE models trained with different numbers of batches for (**a**) resin viscosity prediction and (**b**) resin acidity number prediction. +: They are part of box plot, they are outliers in the residuals. From Table 2, the results of training with 1 batch for resin acidity number prediction, show that MoLE-Lasso performs better with an average \(R^{2}=0.44\). On the other hand, the performance of resin viscosity prediction with 1 batch has better results for MoLE-EN, with a value of \(R^{2}=0.76\). This shows that the resin viscosity can be predicted even with few data for training. From the boxplot, Figure 2, the MoLE-Lasso and MoLE-EN have the lowest variance on resin viscosity prediction, while for resin acidity number the variance of prediction is higher. Figure 2, exhibits that the performance of all models increases with the number of batches used for training, as well the variance decreases. An interesting observation is related to the Mix-PLS performance, which shows a high variance of performance for small batches, which decreases as the number of training batches increases. For 20 batches it performs quite similar to, or even better than, Lasso regularization. This suggests that Mix-PLS can be a valid option when dealing with a large number of samples (in our experiment, more than 400 samples). Overall, RR regularization performs poorly among the experiments. This is reinforced by results in Table 2, where MoLE-RR provides the worst results in the majority of experiments. Overall, all regularized MoLE performed well in the experiments.