COVAriance-Induced Fairness Gap Penalty for Subgroup-Fair Clustering

2026-07-20

AI Summary

This work addresses the challenges posed by the combinatorial explosion of subgroups when multiple sensitive attributes are present, a setting in which existing fair clustering methods suffer from high computational cost, numerical instability, and difficulty handling sparse subgroups. The authors propose COVA-FC, an algorithm that introduces, for the first time, a covariance-based proxy metric strictly equivalent to subgroup fairness disparity and enables efficient gradient-based optimization through continuous relaxation. COVA-FC simultaneously enforces both subgroup and marginal fairness, reveals that neither notion implies the other, and establishes a unified optimization framework for their joint satisfaction. Experiments demonstrate that COVA-FC achieves significantly improved computational efficiency across multiple benchmark datasets while delivering superior trade-offs between clustering cost and fairness under both subgroup and higher-order marginal fairness constraints.

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.

Problem

• fair clustering
• subgroup fairness
• sensitive attributes
• computational efficiency
• marginal fairness

Innovation

• subgroup fairness
• covariance-based surrogate
• continuous relaxation
• gradient-based optimization
• fair clustering