Differential Privacy has Bounded Impact on Fairness in Classification

Paul Mangold, Michaël Perrot, Aurélien Bellet, Marc Tommasi
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:23681-23705, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-mangold23a, title = {Differential Privacy has Bounded Impact on Fairness in Classification}, author = {Mangold, Paul and Perrot, Micha\"{e}l and Bellet, Aur\'{e}lien and Tommasi, Marc}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {23681--23705}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/mangold23a/mangold23a.pdf}, url = {https://proceedings.mlr.press/v202/mangold23a.html}, 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.} }
Endnote
%0 Conference Paper %T Differential Privacy has Bounded Impact on Fairness in Classification %A Paul Mangold %A Michaël Perrot %A Aurélien Bellet %A Marc Tommasi %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-mangold23a %I PMLR %P 23681--23705 %U https://proceedings.mlr.press/v202/mangold23a.html %V 202 %X 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.
APA
Mangold, P., Perrot, M., Bellet, A. & Tommasi, M.. (2023). Differential Privacy has Bounded Impact on Fairness in Classification. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:23681-23705 Available from https://proceedings.mlr.press/v202/mangold23a.html.

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