# Stability of Feature Selection in Multi-Omics Data Analysis
###### Abstract
Among the embedded methods, feature selection is most commonly performed by techniques based on the L1 norm (such as Lasso regression) and decision tree-based methods (such as Random Forest), both of which incorporate feature selection into the model-fitting process [23]. In contrast, feature selection can also be done as a separate step (prior to model training), but such an approach still often requires building a classifier on the selected features to evaluate its performance, ultimately linking the quality of feature selection with the classifier's performance. The importance of feature selection in multi-omics data has been well recognized, and several studies have benchmarked various feature-selection methods. For instance, [PERSON] et al. [24] conducted a large-scale benchmark experiment comparing different feature-selection methods, providing valuable insights into the effectiveness of various approaches. The benchmark was based on 15 cancer datasets from TCGA [8]. According to the authors, no such benchmark was performed before their work. After literature inquiry, including [25, 26], they chose the following 8 feature-selection methods (the most frequently used in context of cancer classification): T-test [27], Information gain (infor) [28], Relieff [29], Minimum Redundancy Maximum Relevance (mRMR) [30], Recursive Feature Elimination (RFE) [31], Genetic Algorithm (GA) [32], Least Absolute Shrinkage and Selection Operator (Lasso) [33], and permutation importance of Random Forest (RF-VI) [34]. In order to assess the predictive performance, accuracy, and the AUC, the Brier test was used. [PERSON]'s test was applied to test for differences between the dataset-specific performance measure values obtained with different methods. [PERSON] et al. [24] concluded that feature selection is an especially important topic, as the proper selection of data features may improve prediction accuracy and reduce the complexity of machine-learning models. Based on the benchmark results, the following main statements were made: (1) RF-VI (method of embedded type [34]) and mRMR(method of filter type [30]) can be used, where it is sufficient to use only small numbers of best features; (2) Lasso (method of embedded type [33]) provides comparable or slightly better predictive performance when compared to the previously mentioned methods, although models have a noticeably bigger number of features; (3) the mRMR method is computationally expensive. Unfortunately, the authors focused on predictive accuracy, missing another important aspect, that of stability of feature selection, which creates another gap in the research. Specifically, it remains unclear how consistent and reliable the selected features are across various classification models and datasets. To sum things up, the importance lies in the better reproducibility of findings derived from multi-omics analyses and better resiliency to minor changes in the training dataset. The stability of feature selection is an emerging topic. [PERSON] and [PERSON] [35] provided a review of works concerning feature-selection techniques, keeping in mind different sources of instability and the high dimensionality of data. They noted that a high correlation of features may frequently produce multiple equally optimal signatures, reducing the confidence of selected features. Up-to-date analysis and comparison of feature-selection methods were provided by [PERSON] et al. [36]. They focused on comparing different stability metrics, claiming their work to be an extensive and complete review of feature-selection algorithms and their evaluation. They mention challenges like high-dimensional data, small samples, noisy and redundant features, and biased data. Metrics for selection accuracy, selection redundancy, prediction performance, algorithmic stability, selection reliability, and computational time were employed. Furthermore, [PERSON] and [PERSON] [37] showed the shortcomings of existing stability metrics, unable to properly address data drift or non-uniformly distributed missing values.