Although many fairness criteria have been proposed to ensure that machine learning algorithms do not exhibit or amplify our existing social biases, these algorithms are trained on datasets that can themselves be statistically biased. In this paper, we investigate the robustness of a number of existing (demographic) fairness criteria when the algorithm is trained on biased data. We consider two forms of dataset bias: errors by prior decision makers in the labeling process, and errors in measurement of the features of disadvantaged individuals. We analytically show that some constraints (such as Demographic Parity) can remain robust when facing certain statistical biases, while others (such as Equalized Odds) are significantly violated if trained on biased data. We also analyze the sensitivity of these criteria and the decision maker's utility to biases. We provide numerical experiments based on three real-world datasets (the FICO, Adult, and German credit score datasets) supporting our analytical findings. Our findings present an additional guideline for choosing among existing fairness criteria, or for proposing new criteria, when available datasets may be biased.

翻译：尽管已有诸多公平性标准被提出，以确保机器学习算法不会展现或放大我们现有的社会偏见，但这些算法所训练的数据集本身就可能存在统计偏差。本文研究了当算法基于有偏数据训练时，若干现有（人口统计）公平性标准的鲁棒性。我们考虑两类数据集偏差：先前决策者在标签过程中产生的误差，以及弱势群体特征测量中的误差。通过理论分析，我们发现某些约束条件（如人口均衡）在面对特定统计偏差时仍能保持鲁棒性，而其他约束条件（如几率均等）在基于有偏数据训练时则会显著违背。我们还分析了这些标准及决策者效用的偏差敏感性。基于FICO、成人收入和德国信用评分三个真实数据集的数值实验验证了我们的理论分析结果。这些发现为现有公平性标准的选择（或在可用数据集可能存在偏差时提出新标准）提供了额外指导。