On the Impact of Output Perturbation on Fairness in Binary Linear Classification
This work addresses fairness degradation in privacy-preserving ML for binary classification, providing theoretical bounds that are incremental to existing privacy-fairness research.
The paper theoretically analyzes how output perturbation for differential privacy affects individual and group fairness in binary linear classification, showing that fairness impacts are bounded but increase with model dimension for individual fairness and depend on angular margin distributions for group fairness.
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.