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.
From: Zhaoxi Zhang [view email]
[v1]
Mon, 23 Feb 2026 03:35:08 UTC (5,021 KB)
[v2]
Wed, 25 Feb 2026 01:52:46 UTC (5,022 KB)
[v3]
Mon, 29 Jun 2026 15:46:18 UTC (5,792 KB)
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