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arXiv · 2602.19473

The generalized underlap coefficient with an application in clustering

Zhaoxi Zhang·Vanda Inácio·Sara Wade
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Abstract

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.

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Zhaoxi Zhang, Vanda Inácio, Sara Wade. 2026-06-29. The generalized underlap coefficient with an application in clustering. https://arxiv.org/abs/2602.19473

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