On the Impact of Output Perturbation on Fairness in Binary Linear
  Classification
Vitalii Emelianov Michaël Perrot
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.