## 3 Results and Discussions
In Table 5, the optimized hyperparameters of our machine learning model are tabulated. A single regression tree always suffers from high variance, meaning that the results can be very different if we randomly split the dataset into two sets at random and fit the regression tree to both of them. Thus, the ensemble method of bagged tree was introduced into the random forest algorithm, which is a procedure to reduce the variance. The bagged tree method is a bootstrap aggregation method that reduces the variance and increases the prediction accuracy by taking repeated N random samples from the training datasets. This produced N regression trees using N bootstrapped training sets, and we then averaged all of the N regression trees. Each regression tree had high variance and low bias with averaging the prediction that reduces variance. In this study, we used the bagged tree method to generate a regression curve with the optimized hyperparameters in Table 5. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Feature Combination** & **Number of Features** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline [PERSON] et al. [20] & 1 & 27.328 & 0.99 \\ [PERSON] et al. +[PERSON] et al. [18, 20] & 2 & **25.418** & 0.99 \\ [PERSON] et al. +[PERSON] et al. +[PERSON] et al. [2, 18, 20] & 3 & 30.326 & 0.99 \\ [PERSON] et al. +[PERSON] et al. +[PERSON] et al. +[PERSON] et al. [2, 18, 20, 22] & 4 & 33.432 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Forward selection of features and the performance of machine learning algorithms for \({}^{112}\)Cd (p, 2n) \({}^{111}\)In [2, 18, 20, 22]. The feature combination that have the lowest RMSE and highest \(\mathbf{R^{2}}\) is highlighted in yellow. Figure 2: Graph of the number of features versus root mean square error (_RMSE_) of (**a**) \({}^{109}\)Ag (\(\alpha\), 2n) \({}^{111}\)In, (**b**) \({}^{111}\)Cd (p, n) \({}^{111}\)In and (**c**) \({}^{112}\)Cd (p, 2n) \({}^{111}\)In nuclear reactions. In Figure 3, we plotted the generated cross-section using an RF algorithm with experimental cross-sections as the input. From Figure 3, we can observe that the regression curve generated by our optimized model shows a good agreement with the TENDL-2019 evaluated data library and the Recommended Nuclear Data for the Production of Selected Therapeutic Radionucleides database results for \({}^{109}\)Ag (\(\alpha\), 2n) \({}^{111}\)In, \({}^{111}\)Cd (p, n) \({}^{111}\)In and \({}^{112}\)Cd (p, 2n) \({}^{111}\)In nuclear reactions, with \(R^{2}\) values between 0.99 and 0.98. This indicates the potential use of a machine learning approach in generating nuclear cross-section data. However, we can observe that the peak of the nuclear cross-section of \({}^{111}\)Cd (p, n) \({}^{111}\)In in Figure 3b is smaller compared to that of the Recommended Nuclear Data for the Production of Selected Therapeutic Radionucleotide database. We suspect that this is  
Figure 3: Generated cross-section using RF algorithm of (**a**) \({}^{109}\)Ag (\(\alpha\), 2n) \({}^{111}\)In, (**b**) \({}^{111}\)Cd (p, n) \({}^{111}\)In and (**c**) \({}^{112}\)Cd (p, 2n) \({}^{111}\)In nuclear reactions. Black line is the TENDL-2019 and Recommended Nuclear Data for the Production of Selected Therapeutic Radionucleotide databases, and red line is our prediction using RF. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Nuclear Reaction** & **Optimized Number of Features** & **Number of Leaves** & **Number of Learners** & **Number of Predictors** \\ \hline
109 Ag (\(\alpha\), 2n) 111 In & 3 & 3 & 27 & 2 \\
111 Cd (p, n) 111 In & 1 & 2 & 30 & 4 \\
112 Cd (p, 2n) 111 In & 2 & 1 & 28 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Hyperparameters of Bayesian optimization. because of the inherent error of each experimental data point used in the training. Thus, we expect that this small deviation can be improved by assigning a weight to each data point used in training based on its experimental error bar.