Fair learning with Wasserstein barycenters for non-decomposable performance measures

Solenne Gaucher, Nicolas Schreuder, Evgenii Chzhen
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:2436-2459, 2023.

Abstract

This work provides several fundamental characterizations of the optimal classification function under the demographic parity constraint. In the awareness framework, akin to the classical unconstrained classification case, we show that maximizing accuracy under this fairness constraint is equivalent to solving a fair regression problem followed by thresholding at level $1/2$. We extend this result to linear-fractional classification measures (e.g., $F$-score, AM measure, balanced accuracy, etc.), highlighting the fundamental role played by regression in this framework. Our results leverage recently developed connection between the demographic parity constraint and the multi-marginal optimal transport formulation. Informally, our result shows that the transition between the unconstrained problem and the fair one is achieved by replacing the conditional expectation of the label by the solution of the fair regression problem. Finally, leveraging our analysis, we demonstrate an equivalence between the awareness and the unawareness setups for two sensitive groups.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-gaucher23a, title = {Fair learning with Wasserstein barycenters for non-decomposable performance measures}, author = {Gaucher, Solenne and Schreuder, Nicolas and Chzhen, Evgenii}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {2436--2459}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/gaucher23a/gaucher23a.pdf}, url = {https://proceedings.mlr.press/v206/gaucher23a.html}, abstract = {This work provides several fundamental characterizations of the optimal classification function under the demographic parity constraint. In the awareness framework, akin to the classical unconstrained classification case, we show that maximizing accuracy under this fairness constraint is equivalent to solving a fair regression problem followed by thresholding at level $1/2$. We extend this result to linear-fractional classification measures (e.g., $F$-score, AM measure, balanced accuracy, etc.), highlighting the fundamental role played by regression in this framework. Our results leverage recently developed connection between the demographic parity constraint and the multi-marginal optimal transport formulation. Informally, our result shows that the transition between the unconstrained problem and the fair one is achieved by replacing the conditional expectation of the label by the solution of the fair regression problem. Finally, leveraging our analysis, we demonstrate an equivalence between the awareness and the unawareness setups for two sensitive groups.} }
Endnote
%0 Conference Paper %T Fair learning with Wasserstein barycenters for non-decomposable performance measures %A Solenne Gaucher %A Nicolas Schreuder %A Evgenii Chzhen %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-gaucher23a %I PMLR %P 2436--2459 %U https://proceedings.mlr.press/v206/gaucher23a.html %V 206 %X This work provides several fundamental characterizations of the optimal classification function under the demographic parity constraint. In the awareness framework, akin to the classical unconstrained classification case, we show that maximizing accuracy under this fairness constraint is equivalent to solving a fair regression problem followed by thresholding at level $1/2$. We extend this result to linear-fractional classification measures (e.g., $F$-score, AM measure, balanced accuracy, etc.), highlighting the fundamental role played by regression in this framework. Our results leverage recently developed connection between the demographic parity constraint and the multi-marginal optimal transport formulation. Informally, our result shows that the transition between the unconstrained problem and the fair one is achieved by replacing the conditional expectation of the label by the solution of the fair regression problem. Finally, leveraging our analysis, we demonstrate an equivalence between the awareness and the unawareness setups for two sensitive groups.
APA
Gaucher, S., Schreuder, N. & Chzhen, E.. (2023). Fair learning with Wasserstein barycenters for non-decomposable performance measures. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:2436-2459 Available from https://proceedings.mlr.press/v206/gaucher23a.html.

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