Algorithmic Fairness is an established area of machine learning, willing to reduce the influence of hidden bias in the data. Yet, despite its wide range of applications, very few works consider the multi-class classification setting from the fairness perspective. We focus on this question and extend the definition of approximate fairness in the case of Demographic Parity to multi-class classification. We specify the corresponding expressions of the optimal fair classifiers. This suggests a plug-in data-driven procedure, for which we establish theoretical guarantees. The enhanced estimator is proved to mimic the behavior of the optimal rule both in terms of fairness and risk. Notably, fairness guarantees are distribution-free. The approach is evaluated on both synthetic and real datasets and reveals very effective in decision making with a preset level of unfairness. In addition, our method is competitive (if not better) with the state-of-the-art in binary and multi-class tasks.

翻译：算法公平性已成为机器学习中一个成熟的研究领域，旨在减少数据中隐藏偏差的影响。然而，尽管其应用范围广泛，目前很少有研究从公平性角度考虑多分类设置。我们聚焦于这一问题，将群体公平性中近似公平的定义扩展至多分类场景，并推导出最优公平分类器的相应表达式。由此提出一种基于插入法的数据驱动程序，并为其建立了理论保障。改进后的估计器被证明能够在公平性和风险两方面模仿最优规则的行为。值得注意的是，公平性保证是分布无关的。该方法在合成数据集和真实数据集上均进行了评估，在预设不公平程度下的决策过程中表现出色。此外，我们的方法在二分类和多分类任务中与现有最优方法相比具有竞争力（即便不是更优）。