# The generalized underlap coefficient with an application in clustering

arXiv: https://arxiv.org/abs/2602.19473 · HTML: https://mlsanity.com/paper/2602.19473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [A Comprehensive Survey of Mixture-of-Experts: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2503.07137/) (2025)
- [A Review of Feature Selection Methods Based on Mutual Information](https://mlsanity.com/paper/1509.07577/) (2015)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Bayesian cluster analysis: Point estimation and credible balls](https://mlsanity.com/paper/1505.03339/) (2015)
- [Evaluating State-of-the-Art Classification Models Against Bayes Optimality](https://mlsanity.com/paper/2106.03357/) (2021)
- [The Dependent Dirichlet Process and Related Models](https://mlsanity.com/paper/2007.06129/) (2020)
- [Bayesian dependent mixture models: A predictive comparison and survey](https://mlsanity.com/paper/2307.16298/) (2023)
- [Density regression via Dirichlet process mixtures of normal structured additive regression models](https://mlsanity.com/paper/2401.03881/) (2024)
- [The underlap coefficient as a measure of a biomarker's discriminatory ability](https://mlsanity.com/paper/2504.12288/) (2025)

## Abstract (arXiv)

Quantifying distributional separation across groups is fundamental in statistical learning and scientific discovery, yet most classical discrepancy measures are tailored to two-group comparisons. We generalize the underlap coefficient (UNL), a multi-group separation measure, to multivariate settings. We study its relationship with Bayes risk and mutual information, and further interpret the UNL as a measure of dependence between group labels and variables of interest. We propose an efficient importance sampling estimator of the UNL that can be combined with flexible density estimation methods. A key application is the assessment of partition-covariate dependence in clustering, where the UNL provides an interpretable measure of whether latent group structure can be explained by specific covariates. The methodology is illustrated on two real-world datasets.