# When to Truncate a Feature Ranking: A Residual-Overlap Stopping Rule for Subset Selection

arXiv: https://arxiv.org/abs/2606.31686 · HTML: https://mlsanity.com/paper/2606.31686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 53 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Infinite Feature Selection: A Graph-based Feature Filtering Approach](https://mlsanity.com/paper/2006.08184/) (2020)
- [Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means](https://mlsanity.com/paper/1401.4788/) (2014)
- [Understanding the classes better with class-specific and rule-specific feature selection, and redundancy control in a fuzzy rule based framework](https://mlsanity.com/paper/2208.01294/) (2022)
- [Feature Selection via Maximizing Distances between Class Conditional Distributions](https://mlsanity.com/paper/2401.07488/) (2024)
- [XNB: Explainable Class-Specific NaIve-Bayes Classifier](https://mlsanity.com/paper/2411.01203/) (2024)
- [Feature Selection Based on Wasserstein Distance](https://mlsanity.com/paper/2411.07217/) (2024)

## Abstract (arXiv)

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.