# Integrating Multi-Omics Using Bayesian Ridge Regression with Iterative Similarity Bagging
###### Abstract
Given that most omics data have a small number of samples, which are considered small-scale, Bayesian analysis is appropriate for such scenarios [27]. However, the BRR output datasets contain many features, leading to complexity and dimensionality issues. More details will be elaborated on in the Results and Discussion section. Therefore, Iterative Similarity Bagging (ISB) was introduced as the next step in solving these problems. Iterative Similarity Bagging was inspired by the bagging ensemble technique, utilizing column-based grouping to set features in bags without replacement [28]. The similarity is then computed based on a Euclidean distance for each group's features or genes. The nearest features inside each bag are considered redundant and are removed according to a dynamic threshold. ISB is an unsupervised method that dynamically reduces dimensionality without losing the original biological values. By preserving interpretability and retaining the original values, ISB helps to measure the relationships between drug response and omics features, as well as between the omics features themselves. Therefore, features are studied and selected according to their original values without transforming them into new features [28]. Furthermore, there is a strong correlation between features represented by probes with either similar molecular activities (as shown in gene expression analysis) or genomic positions (as observed in DNA copy number analysis) [29]. Traditional machine learning and feature selection techniques exhibit instability when confronted with strong correlations across features [29; 30]. [PERSON] et al. [31] examined the influence of correlated features in large-scale omics datasets by employing a random forest model with a recursive feature elimination technique. The researchers determined that RF-RFE may not be suitable for dealing with high-dimensional omics data containing numerous highly correlated features [31]. The contribution of this paper can be summarized in the following points:  
1. Bayesian Ridge Regression (BRR) is introduced as a supervised domain-oriented feature selection method to reduce omics complexity and dimensionality. Features are selected based on domain contexts, such as drug response and cancer classification. 2. A new method named Iterative Similarity Bagging (ISB) is presented to perform a dynamic reduction of dimensionality and complexity without losing the biological measurements of omics data, which is a common issue with some transformation-based integration approaches. This study presents BRR-ISB, a method that discovers informative features by utilizing two relationships. The first relationship focuses on drug response and multi-omics types, exploring how drug response can be predicted using multi-omics features. Bayesian RidgeRegression (BRR) is used to study this relationship. BRR is a supervised feature selection method that ranks features according to their relevance to drug response. By estimating coefficients for all its features, BRR can identify influential ones on drug response, ensuring these selected features are contextually meaningful. The following relationship studies the connections among omics features themselves. It is assessed via Iterative Similarity Bagging (ISB), an unsupervised approach that removes similar genes based on their distance metrics. ISB works by iteratively pruning the feature set, selecting the most similar ones, and leaving others that are more distinctively informative. This paper combines these two approaches to produce a more robust model for predicting drug response, thereby balancing domain-specific relevance and internal feature variety. The rest of this manuscript is structured as follows: Section 2 introduces the related studies. Section 3 details the methods and materials utilized in this investigation, including the datasets, BRR, ISB, and evaluation metrics. Section 4 elaborates on the results and discussion. Finally, Section 5 presents the conclusion, limitations, and future work.