# Integrating Multi-Omics Using Bayesian Ridge Regression with Iterative Similarity Bagging
## 4 Results and Discussion
### Effectiveness of BRR-ISB in Drug Response Prediction
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline
**Method** & **Input Features** & **Model Features** & **Training** & & & **Validation** & & **Testing** & & **Time** \\ \hline  & & & RMSE & PCC & R\({}^{2}\) & RMSE & PCC & R\({}^{2}\) & RMSE & PCC & R\({}^{2}\) & \\ \hline Baseline & 46,016 & 46,016 & 0.088 & 0.935 & 0.873 & 0.12 & 0.864 & 0.744 & 0.13 & 0.13 & 0.737 & 403:11 \\ \hline  & & & \multicolumn{4}{c}{Iterative Similarity Bagging (ISB)} & & & & & & & \\ \hline ISB bag size = 50, & 46,016 & 13,844 & 0.087 & 0.935 & 0.875 & 0.118 & 0.871 & 0.755 & 0.126 & 0.87 & 0.754 & 10:17 \\ \hline ISB bag size = 50, & 46,016 & 12,270 & 0.103 & 0.909 & 0.824 & 0.127 & 0.847 & 0.716 & 0.13 & 0.858 & 0.736 & 9:16 \\ \hline ISB bag size = 100, & 46,016 & 5926 & 0.08 & 0.946 & 0.894 & 0.117 & 0.87 & 0.755 & 0.129 & 0.862 & 0.74 & 5:50 \\ \hline ISB bag size = 200, & 46,016 & 2390 & 0.091 & 0.929 & 0.863 & 0.116 & 0.875 & 0.764 & 0.124 & 0.873 & 0.76 & 3:51 \\ \hline ISB bag size = 300, & 46,016 & 2261 & 0.091 & 0.929 & 0.863 & 0.119 & 0.866 & 0.747 & 0.126 & 0.868 & 0.75 & 3:48 \\ \hline ISB bag size = 400, & 46,016 & 2119 & 0.1 & 0.917 & 0.837 & 0.119 & 0.866 & 0.75 & 0.127 & 0.865 & 0.747 & 3:42 \\ \hline  & & \multicolumn{4}{c}{Bayesian Ridge Regression with Iterative Similarity Bagging (BRR-ISB)} & & & & & & & & & \\ \hline BRR & 23,683 & 23,683 & 0.087 & 0.937 & 0.877 & 0.117 & 0.872 & 0.758 & 0.125 & 0.87 & 0.754 & 15:43 \\ \hline BRR-ISB bag size = 50, & 23,683 & 5740 & 0.093 & 0.926 & 0.857 & 0.115 & 0.876 & 0.766 & 0.124 & 0.872 & 0.759 & 5:48 \\ \hline BRR-ISB bag size = 50, & 23,683 & 4822 & 0.094 & 0.924 & 0.854 & 0.121 & 0.86 & 0.739 & 0.127 & 0.865 & 0.748 & 5:20 \\ \hline BRR-ISB bag size = 100, & 23,683 & 2133 & 0.099 & 0.917 & 0.84 & 0.117 & 0.871 & 0.758 & 0.125 & 0.869 & 0.754 & 3:57 \\ \hline BRR-ISB bag size = 200, & 23,683 & 1273 & 0.097 & 0.919 & 0.845 & 0.114 & 0.879 & 0.771 & 0.121 & 0.879 & 0.77 & 3:50 \\ \hline BRR-ISB bag size = 300, & 23,683 & 1245 & 0.099 & 0.918 & 0.84 & 0.116 & 0.872 & 0.76 & 0.122 & 0.877 & 0.768 & 3:47 \\ \hline BRR-ISB bag size = 400, & 23,683 & 1260 & 0.097 & 0.921 & 0.846 & 0.116 & 0.874 & 0.763 & 0.127 & 0.867 & 0.749 & 3:50 \\ \hline  & & \multicolumn{4}{c}{Similarity Network Fusion} & & & & & & & & & \\ \hline SNF & 46,016 & 363 & 0.13 & 0.854 & 0.721 & 0.13 & 0.841 & 0.699 & 0.134 & 0.848 & 0.716 & 3:02 \\ \hline BRR-SNF & 23,683 & 363 & 0.126 & 0.859 & 0.738 & 0.127 & 0.844 & 0.713 & 0.138 & 0.847 & 0.7 & 3:02 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The scenarios were implemented using the same CCLE dataset and drug chemical structure for drug response prediction. integration method, may decrease the interpretability of a model due to the potential loss of biological context in the extracted features. In contrast, BRR-ISB, with its dynamic reduction in dimensionality and complexity without compromising the biological measurements of omics data, outperformed SNF regarding RMSE, PCC, R2, and execution time. In addition to a reduction in computational cost and a substantial dimension reduction, the feature selection methods offer several benefits. These benefits include enhanced model interpretability, reduced overfitting risk, and potentially improved generalization to new data. Studying multi-omics with a few informative features can facilitate interpretability and discovering relationships between variables. Furthermore, BRR-ISB demonstrated no overfitting between training and validation, as depicted in Figure 5, which shows the loss values between training and validation in the BRR-ISB scenario with a bag size of 200 and ten iterations. This study addresses overfitting through several approaches. Regularization is a feature embedded within BRR that prevents overfitting and enhances the model's ability to generalize, particularly when multicollinearity or high-dimensional data are present [89]. In addition, ISB works iteratively to select essential features by removing highly correlated