# Integrating Multi-Omics Using Bayesian Ridge Regression with Iterative Similarity Bagging
## 5 Conclusions  
This paper introduced BRR-ISB as a multi-omics integration method aimed at overcoming challenges such as dimensionality and the loss of biological context inherent in transformation-based methods. Bayesian Ridge Regression (BRR) was proposed as a supervised approach for feature selection in omics to reduce complexity and dimensionality. Features were selected based on domain-specific contexts, such as drug response and cancer classification. The Iterative Similarity Bagging (ISB) method was introduced to further reduce omics data's dimensionality and complexity without compromising the biological measurements. This methodology addresses the limitations associated with transformation-based integration methods. Various scenarios were employed to evaluate the efficacy of BRR-ISB in drug response prediction. The scenario used for BRR-ISB, utilizing a bag size of 200 features and conducting ten iterations, had superior performance in terms of RMSE, PCC, and R\({}^{2}\) when compared to other scenarios. Furthermore, the execution time was reduced by 77% compared to the BRR scenario. SNF is a transformation-based integration method that converts omics types into a new representation. However, this transformation might decrease a model's interpretability, as the extracted features may lose their biological context. Moreover, BRR-ISB, a method that effectively reduces the dimensionality and complexity of omics data while preserving biological measurements, shows improvement compared to SNF regarding RMSE, PCC, R\({}^{2}\), and execution time. Furthermore, the BRR-ISB model demonstrated no overfitting between the training and validation datasets. This was observed by comparing the loss values in the BRR-ISB scenario, which involved 200 bag sizes and ten iterations. However, there are some limitations of the BRR-ISB. BRR is a wrapper feature selection method that is considered time-consuming. It can be replaced by other filter feature selection methods suitable for small-scale datasets. Wrapper feature selection approaches are perceived as time-consuming since they include iterations, necessitate model training, and explore a vast search space [94]. These techniques entail the training and assessment of several models, each utilizing a distinct set of features. Cross-validation is typically employed to ensure the reliability and stability of the results. Exploring the extensive range of potential feature combinations can be computationally demanding, particularly for datasets with several features, resulting in a longer computation time. In addition, wrapper approaches can utilize iterative algorithms to continuously modify the feature subsets based on their impact on model performance [94,95]. Furthermore, features from the CCLE and GDSC were selected manually using either BRR-ISB or ISB alone. Therefore, the process of selecting the optimal number that represented informative features was not precise. In future work, different filter feature selection methods need to be investigated as an alternative to Bayesian Ridge Regression that may reduce the time requirement and complexity of BRR. In addition, more data, such as methylation and metabolomics data, may need to be investigated to integrate them using ISB to improve drug response prediction. Furthermore, the current study utilized the half-mean as a threshold of the \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model** & **RMSE** & **PCC** & **R\({}^{2}\)** \\ \hline WGRMF & 0.56 & 0.72 & - \\ EBSRMF & 0.21 & 0.86 & \\ DeepDSC & 0.23 & - & 78 \\ SRMF & 0.57 & 0.71 & \\ BRR-ISB (Proposed) & 0.12 & 0.879 & 77 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of performances with other related studies. ISB; different thresholds, such as mean, median, and first percentile Q1, will be tested and compared. Other distance metrics, such as the Manhattan distance and Pearson correlation, will also be studied to improve the effectiveness of ISB. Conceptualization, K.H.A. and N.A.A. ; Methodology, T.M.A. and N.A.A. ; Software, T.M.A.