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This research introduces COVA-FC, a novel algorithm that uses covariance-based surrogates to efficiently optimize fairness constraints in clustering tasks involving exponentially large subgroups. By addressing numerical instability inherent in traditional methods, the approach offers improved computational efficiency and better cost-fairness trade-offs on benchmark datasets. The work advances machine learning theory by formally distinguishing between subgroup-level and marginal fairness gaps within unsupervised learning contexts.
COVAriance-Induced Fairness Gap Penalty for Subgroup-Fair Clustering
arXiv:2607.18119v1 Announce Type: cross Abstract: Fair clustering aims to make cluster assignments independent of sensitive attributes, but this goal becomes challenging when multiple sensitive attributes jointly define many subgroups. In such settings, directly extending existing fair clustering algorithms is computationally expensive or numerically unstable, especially when the number of subgroups grows exponentially and some subgroups contain only a few instances. To address these challenges, we define a subgroup-fairness gap for clustering and derive a covariance-based surrogate that exactly matches this gap. We then introduce a continuous relaxation of the surrogate, enabling efficient gradient-based optimization and yielding our proposed algorithm, COVA-FC. We also show that subgroup fairness alone does not imply marginal fairness, and extend our framework to capture a subgroup-marginal-fairness gap. Experiments on benchmark datasets show that COVA-FC achieves competitive cost-fairness trade-offs and improves computational efficiency over existing baselines in both subgroup and higher-order marginal settings.
Abstract:Fair clustering aims to make cluster assignments independent of sensitive attributes, but this goal becomes challenging when multiple sensitive attributes jointly define many subgroups. In such settings, directly extending existing fair clustering algorithms is computationally expensive or numerically unstable, especially when the number of subgroups grows exponentially and some subgroups contain only a few instances. To address these challenges, we define a subgroup-fairness gap for clustering and derive a covariance-based surrogate that exactly matches this gap. We then introduce a continuous relaxation of the surrogate, enabling efficient gradient-based optimization and yielding our proposed algorithm, COVA-FC. We also show that subgroup fairness alone does not imply marginal fairness, and extend our framework to capture a subgroup-marginal-fairness gap. Experiments on benchmark datasets show that COVA-FC achieves competitive cost-fairness trade-offs and improves computational efficiency over existing baselines in both subgroup and higher-order marginal settings.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2607.18119 [stat.ML]
(or arXiv:2607.18119v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.18119 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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