Stochastic Sequential Search in Very-High-Dimensional Feature Selection

Background: Since 1990 many feature selection methods have been proposed across heterogeneous applications. To validate the usefulness of a new method, it needs to be compared against at least one baseline method from the existing literature on a feature selection task using at least one dataset. Recent developments in tabular Deep Learning (DL) and data valuation in Machine Learning (ML) suggest that the evaluation of new methods, algorithms, and models may be consciously or unconsciously biased. We hypothesise that a similar trend exists in feature selection (FS), particularly in filter feature selection (FFS). The aim of this study is therefore to examine FFS studies to identify factors that influence the evaluation and that might consist entry point for biases in order to recommend stronger principles for FFS evaluation. Methods: We analyse a sample of 28 high profile FFS studies published between 1994 and 2025. The analysis provides reflections on how to examine FFS studies, highlights lessons learned throughout the process, and gives five evidence-based recommendations for future FFS evaluation. Results: Multivariate Linear Regression analysis achieved a score of $R^2=0.33$. It means that 33% of the variance in the performance of new methods against chosen baselines (win rate) is explained by the number of datasets (#Datasets), the number of baselines (#Baselines), and the number of new methods (#NewMethods). Discussion: $R^2=0.33$ is considered medium explanation; which is promising given that this is the first such study. The medium explanation result is due to the fact that win rate is influenced by additional factors such as the maturity of the feature selection domain, the type of datasets and baselines, and the simplicity of the regression model used to explain the relationship.

Feature rankings are widely used in supervised feature selection because they are simple, scalable and easy to interpret. Variables are first ranked by a relevance score, and a subset is then obtained by retaining the top-ranked variables. Although the first stage has been extensively studied, the second is often governed by an arbitrary cardinality, an empirical threshold or cross-validation, without a direct interpretation. This raises a basic question: given a feature ranking, when is there enough accumulated class-separation evidence to stop selecting features? This paper develops a distributional framework for transforming supervised feature rankings into class-independent subsets through an explicit risk-calibrated stopping rule. For each variable and each pair of classes, marginal separation is measured by the Bhattacharyya coefficient between the corresponding class-conditional distributions. The proposed method selects a single global subset shared by all classes by retaining the shortest prefix of a ranking whose residual product overlap falls below a prescribed threshold for every relevant class contrast. We derive binary and multiclass Bayes-risk bounds for the labelled product marginal problem, and obtain prior-dependent and prior-free calibrations of the residual-overlap threshold from a target all-pairs risk level. An empirical comparison on high-dimensional genomic datasets illustrates that the rule can reduce tens of thousands of variables to a few dozen while maintaining predictive performance statistically comparable to the all-features baseline. As the stopping rule only requires one-dimensional marginal overlap estimates and scans a precomputed ranking, it is well suited to very high-dimensional settings where exhaustive subset search is infeasible and interpretable truncation of feature rankings is essential.

Feature selection is a fundamental machine learning and data mining task, involved with discriminating redundant features from informative ones. It is an attempt to address the curse of dimensionality by removing the redundant features, while unlike dimensionality reduction methods, preserving explainability. Feature selection is conducted in both supervised and unsupervised settings, with different evaluation metrics employed to determine which feature selection algorithm is the best. In this paper, we propose FSEVAL, a feature selection evaluation toolbox accompanied with a visualization dashboard, with the goal to make it easy to comprehensively evaluate feature selection algorithms. FSEVAL aims to provide a standardized, unified, evaluation and visualization toolbox to help the researchers working in the field, conduct extensive and comprehensive evaluation of feature selection algorithms with ease.