Differential Privacy has Bounded Impact on Fairness in Classification

• URL: http://arxiv.org/abs/2210.16242v3
• Date: Mon, 18 Sep 2023 10:25:49 GMT
• Title: Differential Privacy has Bounded Impact on Fairness in Classification
• Authors: Paul Mangold, Micha\"el Perrot, Aur\'elien Bellet, Marc Tommasi
• Abstract summary: We 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.
• Score: 7.022004731560844
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 this Lipschitz property to prove a non-asymptotic bound showing that, as the number of samples increases, the fairness level of private models gets closer to the one of their non-private counterparts. This bound also highlights the importance of the confidence margin of a model on the disparate impact of differential privacy.

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