We theoretically study the impact of differential privacy on fairness in classification. We prove that, given a class of models, popular group fairness measures are pointwise Lipschitz-continuous with respect to the parameters of the model. This result is a consequence of a more general statement on accuracy conditioned on an arbitrary event (such as membership to a sensitive group), which may be of independent interest. We use the aforementioned Lipschitz property to prove a high probability bound showing that, given enough examples, the fairness level of private models is close to the one of their non-private counterparts.

翻译：我们从理论上研究了差分隐私对分类公平性的影响。我们证明，给定一类模型，常见的群体公平性度量在模型参数上是逐点利普希茨连续的。这一结果源于一个更一般性的关于任意事件（如属于敏感群体）条件下准确率的陈述，该陈述本身可能具有独立的研究价值。我们利用上述利普希茨性质，证明了一个高概率界：在给定足够样本的情况下，隐私模型的公平性水平与其非隐私对应模型的公平性水平接近。