Differential Privacy has Bounded Impact on Fairness in Classification
This addresses fairness concerns for machine learning practitioners using differential privacy, though it is incremental as it builds on existing theoretical frameworks.
The paper tackles the problem of how differential privacy affects fairness in classification, proving that fairness measures are Lipschitz-continuous and providing a non-asymptotic bound showing private models' fairness approaches non-private models as sample size increases.
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.