# Integrating Multi-Omics Using Bayesian Ridge Regression with Iterative Similarity Bagging
###### Abstract
Most studies utilized feature selection methods to reduce the dimensionality and complexity associated with the early integration approach [11; 12]. The middle integration approach reduces the complexity of omics by transforming them into a simple or low-dimensional representation [6]. Each dataset is independently transformed into a new representation and then combined with others before the learning process [7]. This approach employs various techniques, such as graph-embedding [13;14], network-based methods [15; 16; 17], and kernel-based methods [18; 19; 20]. Graph embedding focuses on modeling each dataset using a graph by learning a low-dimensional representation of the nodes and their relationships [7]. The network-based approach transforms each dataset and fuses them into a homogeneous network [12]. The kernel-based approach involves creating a kernel to integrate multiple omics blocks for each omics dataset and then combining them in a single matrix [7;21]. Late integration consists of multiple layers, with each layer in the model representing a single omics dataset [6]. Each layer analyzes its data independently without combining all other types. Integration occurs at the results level or by using fully connected layers, as in neural networks or deep learning models [6]. Consequently, the \"curse of dimensionality\"--having many features (p) and few available data samples (n)--is among the most challenging when dealing with omics or biological data [12]. Therefore, the limited number of data instances (n) and the large number of features (p) present significant hurdles to adopting early concatenation in multi-omics integration [6]. Additionally, most studies introduce unsupervised methods that integrate multi-omics without considering domain contexts such as drug response and cancer classification [22]. In addition, transforming omics data types into a new representation reduces the interpretability of a model because the extracted features may lose the biological context [7]. Transformation-based methods frequently include complex mathematical transformations or fusion processes, which can lead to less interpretability of the models. Consequently, understanding the precise biological measurements of features or relationships within the integrated data might be challenging [7; 23]. The reduction in interpretability from transformation-based multi-omics integration refers to the loss of understanding of biological values when raw biological data are converted into abstract features using elaborate transformations [7]. This reduction occurs because the produced features do not directly relate to the original biological variables (e.g., genes or proteins). For example, methods like variational autoencoders and Similarity Network Fusion (SNF) [24] generate new features from the original ones, with new values that do not reflect the original biological variables. This loss of interpretability makes it challenging to map model predictions back to precise biological processes or mechanisms, thus obscuring direct biological relevance and hindering meaningful inferences from the model output. Consequently, transformation methods tend to mask intrinsic relationships within raw data--relationships that are often pivotal in uncovering valuable insights for biomedical research. This paper introduces a new method called Iterative Similarity Bagging (ISB), supported by Bayesian Ridge Regression (BRR) as a domain-oriented feature selection method. Drug response is assigned to each omics type as an input for BRR. Subsequently, BRR works as a domain-oriented supervised feature selection tool to choose essential features by calculating the coefficient for each feature. Bayesian regression estimates linear models using probability distributions rather than singular point values [25]. The posterior probability of the model parameters depends on training inputs and outcomes [25]. The Ridge approach is used with Bayesian regression to reduce model complexity and multicollinearity through coefficient reduction [26].