标题： 设定公平性：用于集合值分类的群体公平约束 显示英文标题

标题： Set to Be Fair: Demographic Parity Constraints for Set-Valued Classification

摘要： 在多类设置中使用集合值分类，当类别之间可能发生混淆时，会导致误导性预测。 然而，其应用可能会加剧歧视性偏差，从而促使在公平性约束下开发集合值方法。 在本文中，我们研究了在人口均等性和期望大小约束下的集合值分类问题。 我们提出了两种互补策略：一种基于oracle的方法，在满足两个约束的同时最小化分类风险；另一种是计算高效的代理方法，优先考虑约束的满足。 对于这两种策略，我们推导了（最优）公平集合值分类器的显式表达式，并利用这些表达式构建了用于经验预测的插件、数据驱动程序。 我们建立了两种方法在大小和公平性约束违反方面的无分布收敛率，在较弱假设下，我们也为基于oracle的方法提供了额外风险界限。 实证结果展示了两种策略的有效性，并突出了我们代理方法的效率。 显示英文摘要

摘要： Set-valued classification is used in multiclass settings where confusion between classes can occur and lead to misleading predictions. However, its application may amplify discriminatory bias motivating the development of set-valued approaches under fairness constraints. In this paper, we address the problem of set-valued classification under demographic parity and expected size constraints. We propose two complementary strategies: an oracle-based method that minimizes classification risk while satisfying both constraints, and a computationally efficient proxy that prioritizes constraint satisfaction. For both strategies, we derive closed-form expressions for the (optimal) fair set-valued classifiers and use these to build plug-in, data-driven procedures for empirical predictions. We establish distribution-free convergence rates for violations of the size and fairness constraints for both methods, and under mild assumptions we also provide excess-risk bounds for the oracle-based approach. Empirical results demonstrate the effectiveness of both strategies and highlight the efficiency of our proxy method.