Although the volume of literature and public attention on machine learning fairness has been growing significantly, in practice some tasks as basic as measuring fairness, which is the first step in studying and promoting fairness, can be challenging. This is because sensitive attributes are often unavailable due to privacy regulations. The straightforward solution is to use auxiliary models to predict the missing sensitive attributes. However, our theoretical analyses show that the estimation error of the directly measured fairness metrics is proportional to the error rates of auxiliary models' predictions. Existing works that attempt to reduce the estimation error often require strong assumptions, e.g. access to the ground-truth sensitive attributes or some form of conditional independence. In this paper, we drop those assumptions and propose a framework that uses only off-the-shelf auxiliary models. The main challenge is how to reduce the negative impact of imperfectly predicted sensitive attributes on the fairness metrics without knowing the ground-truth sensitive attributes. Inspired by the noisy label learning literature, we first derive a closed-form relationship between the directly measured fairness metrics and their corresponding ground-truth metrics. And then we estimate some key statistics (most importantly transition matrix in the noisy label literature), which we use, together with the derived relationship, to calibrate the fairness metrics. In addition, we theoretically prove the upper bound of the estimation error in our calibrated metrics and show our method can substantially decrease the estimation error especially when auxiliary models are inaccurate or the target model is highly biased. Experiments on COMPAS and CelebA validate our theoretical analyses and show our method can measure fairness significantly more accurately than baselines under favorable circumstances.

本研究提出一种算法来利用仅有的三个适当识别出的虚拟属性来精确测量公平性和减轻偏见，并展示其允许仅使用虚弱代理来增加用户隐私。

缺失敏感属性的公平性​，使用弱代理足够且更好

缺失敏感属性的公平性，使用弱代理足够且更好