We theoretically study how differential privacy interacts with both individual and group fairness in binary linear classification. More precisely, we focus on the output perturbation mechanism, a classic approach in privacy-preserving machine learning. We derive high-probability bounds on the level of individual and group fairness that the perturbed models can achieve compared to the original model. Hence, for individual fairness, we prove that the impact of output perturbation on the level of fairness is bounded but grows with the dimension of the model. For group fairness, we show that this impact is determined by the distribution of so-called angular margins, that is signed margins of the non-private model re-scaled by the norm of each example.

翻译：我们理论研究了差分隐私如何在二元线性分类中与个体公平性和群体公平性相互作用。具体而言，我们聚焦于输出扰动机制——一种隐私保护机器学习中的经典方法。我们推导了扰动模型相较于原始模型所能达到的个体与群体公平性水平的高概率界。对于个体公平性，我们证明输出扰动对公平性水平的影响虽有界，但随模型维度增长而加剧；对于群体公平性，我们证明该影响由所谓角边际（即非隐私模型经每个样本范数重新缩放后的带符号边际）的分布决定。