Classification with abstention has gained a lot of attention in recent years as it allows to incorporate human decision-makers in the process. Yet, abstention can potentially amplify disparities and lead to discriminatory predictions. The goal of this work is to build a general purpose classification algorithm, which is able to abstain from prediction, while avoiding disparate impact. We formalize this problem as risk minimization under fairness and abstention constraints for which we derive the form of the optimal classifier. Building on this result, we propose a post-processing classification algorithm, which is able to modify any off-the-shelf score-based classifier using only unlabeled sample. We establish finite sample risk, fairness, and abstention guarantees for the proposed algorithm. In particular, it is shown that fairness and abstention constraints can be achieved independently from the initial classifier as long as sufficiently many unlabeled data is available. The risk guarantee is established in terms of the quality of the initial classifier. Our post-processing scheme reduces to a sparse linear program allowing for an efficient implementation, which we provide. Finally, we validate our method empirically showing that moderate abstention rates allow to bypass the risk-fairness trade-off.

中文翻译：

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弃权但无差异的分类

近年来，弃权分类引起了人们的广泛关注，因为它允许将人类决策者纳入该过程。然而，弃权有可能扩大差距并导致歧视性预测。这项工作的目标是建立一种通用分类算法，该算法可以避免预测，同时避免产生不同的影响。我们将此问题形式化为公平和弃权约束下的风险最小化，并以此得出最优分类器的形式。基于此结果，我们提出了一种后处理分类算法，该算法能够仅使用未标记的样本来修改任何基于现成分数的分类器。我们为提出的算法建立了有限的样本风险，公平性和弃权保证。特别是，结果表明，只要有足够多的未标记数据，就可以独立于初始分类器实现公平和弃权约束。风险保证是根据初始分类器的质量确定的。我们的后处理方案简化为一个稀疏的线性程序，可以实现高效执行，这是我们提供的。最后，我们通过经验验证了我们的方法，表明适度的弃权率可以绕过风险与公平的权衡。