Min-Marginal Power Indices for Multi-Objective Feature Selection

Feature selection is a classical problem in statistics and machine learning, and it continues to remain an extremely challenging problem especially in the context of unknown non-linear relationships with dependent features. On the other hand, Shapley values are a classic solution concept from cooperative game theory that is widely used for feature attribution in general non-linear models with highly-dependent features. However, Shapley values are not naturally suited for feature selection since they tend to capture both direct effects from each feature to the response and indirect effects through other features. In this paper, we combine the advantages of Shapley values and adapt them to feature selection by proposing MinShap, a modification of the Shapley value framework along with a suite of other related algorithms. In particular for MinShap, instead of taking the average marginal contributions over permutations of features, considers the minimum marginal contribution across permutations. We provide a theoretical foundation motivated by the faithfulness assumption in DAG (directed acyclic graphical models), a guarantee for the Type I error of MinShap, and show through numerical simulations and real data experiments that MinShap tends to outperform state-of-the-art feature selection algorithms such as LOCO, GCM and Lasso in terms of both accuracy and stability. We also introduce a suite of algorithms related to MinShap by using the multiple testing/p-value perspective that improves performance in lower-sample settings and provide supporting theoretical guarantees.

Unsupervised feature selection is commonly formulated as a multiobjective optimisation problem that jointly optimises subset quality and subset size. Yet the behaviour of this formulation depends critically on the choice of evaluation objective, the direction of subset-size regularisation, and the initialisation strategy. We study these factors in a controlled setting using a synthetic dataset with known informative, redundant, and irrelevant feature types. Six formulations are compared by combining three evaluation objectives: accuracy, silhouette score, and PCA reconstruction loss with subset-size minimisation or maximisation. The results show that formulation strongly affects both search dynamics and the quality of the resulting Pareto front. Silhouette-based formulations exhibit a strong bias toward trivial low-cardinality solutions and remain weak proxies for predictive performance. In contrast, the proposed PCA loss objective produces compact subsets with test accuracy comparable to subsets obtained by directly optimising supervised accuracy. Overall, the study shows that objective design is central to effective multiobjective unsupervised 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.