This paper describes a differentially private post-processing algorithm for learning fair regressors satisfying statistical parity, addressing privacy concerns of machine learning models trained on sensitive data, as well as fairness concerns of their potential to propagate historical biases. Our algorithm can be applied to post-process any given regressor to improve fairness by remapping its outputs. It consists of three steps: first, the output distributions are estimated privately via histogram density estimation and the Laplace mechanism, then their Wasserstein barycenter is computed, and the optimal transports to the barycenter are used for post-processing to satisfy fairness. We analyze the sample complexity of our algorithm and provide fairness guarantee, revealing a trade-off between the statistical bias and variance induced from the choice of the number of bins in the histogram, in which using less bins always favors fairness at the expense of error.

翻译：本文提出了一种差分隐私后处理算法，用于学习满足统计均等性的公平回归器，既解决在敏感数据上训练的机器学习模型的隐私问题，也应对其可能传播历史偏见的公平性问题。该算法通过重映射输出，可对任意给定回归器进行后处理以提升公平性。算法包含三个步骤：首先，通过直方图密度估计和拉普拉斯机制对输出分布进行私有估计，然后计算其Wasserstein重心，最后利用到重心的最优传输进行后处理以满足公平性要求。我们分析了算法的样本复杂度并提供了公平性保障，揭示了直方图分箱数选择所引发的统计偏差与方差之间的权衡关系：分箱数越少，公平性越优，但以误差增加为代价。