We identify a novel connection between the recent literature on multi-group fairness for prediction algorithms and well-established notions of graph regularity from extremal graph theory. We frame our investigation using new, statistical distance-based variants of multi-calibration that are closely related to the concept of outcome indistinguishability. Adopting this perspective leads us naturally not only to our graph theoretic results, but also to new multi-calibration algorithms with improved complexity in certain parameter regimes, and to a generalization of a state-of-the-art result on omniprediction. Along the way, we also unify several prior algorithms for achieving multi-group fairness, as well as their analyses, through the lens of no-regret learning.

翻译：我们在近期关于预测算法多群体公平性的文献与极值图论中经典的图正则性概念之间，发现了一种新颖的联系。本文采用基于统计距离的新型多校准变体（与结果不可区分性概念密切相关）来构建研究框架。这一视角不仅自然引出了我们的图论结论，还催生了在特定参数范围内复杂度更优的新型多校准算法，以及对全预测领域前沿成果的推广。在研究过程中，我们通过无遗憾学习的视角，统一了数种既有的多群体公平性实现算法及其分析框架。