发表机构
Department of Statistics, Seoul National University; KAIST AI（首尔国立大学统计系; 韩国科学技术院人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在多敏感属性定义多个子群时的公平聚类问题，提出基于协方差诱导公平差距惩罚的方法，推导代理并连续松弛，扩展框架捕捉子群 - 边际公平差距，实验证明算法在成本 - 公平权衡上有竞争力且提高计算效率。
AI 中文摘要
公平聚类旨在使聚类分配与敏感属性无关，但当多个敏感属性共同定义多个子群时，这一目标颇具挑战。直接扩展现有公平聚类算法计算成本高或数值不稳定，尤其是子群数量呈指数增长且部分子群实例很少时。为应对这些挑战，我们定义了聚类的子群公平差距并推导了基于协方差的代理，它与该差距完全匹配。接着引入代理的连续松弛，实现基于梯度的高效优化并得出算法COVA - FC。我们还表明子群公平并不意味着边际公平，并扩展框架以捕捉子群 - 边际公平差距。基准数据集实验表明，COVA - FC在成本 - 公平权衡方面具有竞争力，且在子群和高阶边际设置中提高了计算效率。
英文摘要
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.
