Demographic parity (DP) is a widely studied fairness criterion in regression, enforcing independence between the predictions and sensitive attributes. However, constraining the entire distribution can degrade predictive accuracy and may be unnecessary for many applications, where fairness concerns are localized to specific regions of the distribution. To overcome this issue, we propose a new framework for regression under DP that focuses on the tails of target distribution across sensitive groups. Our methodology builds on optimal transport theory. By enforcing fairness constraints only over targeted regions of the distribution, our approach enables more nuanced and context-sensitive interventions. Leveraging recent advances, we develop an interpretable and flexible algorithm that leverages the geometric structure of optimal transport. We provide theoretical guarantees, including risk bounds and fairness properties, and validate the method through experiments in regression settings.
Figures & tables
Figure 1: Illustration for t↦Qs∗(t) for some s∈S in the case where α≤s∈S∑psQf∗∣s(p) (red curve).
Figure 2: Illustration for t↦Qsξ(t) on (p,1] in the case where α>s∈S∑psQf∗∣s(p) (red curve).
Figure 3: Histogram of predictions on synthetic data before (left) and after (right) enforcing (α,p) -DP-tails fairness. The constraint parameters are set (arbitrary) to α=0 , p=0.5
Figure 4: Empirical CDF of the predictions on the synthetic data before and after enforcing DP-tails fairness. Plot (b): the parameters are set (arbitrary) to α=0 , p=0.5 ; plot (c): α=0 and p minimizes ( 7 ).
Figure 5: Evolution of the tail unfairness of g^α,pξ with respect to the size N of the unlabeled dataset on the synthetic data.
Figure 6: Evolution of the MSE and KS distance of g^αξ with respect to α on the synthetic data.
Figure 7: Empirical CDF of the predictions on the Crime before and after enforcing DP-tails fairness. Plot (b): the parameters are set (arbitrary) to α=0.2 , p=0.4 ; Plot (c): α=0.2 and p minimizes ( 7 ). More runs can be seen in Fig. 11 in Appendix C .
Figure 8: Evolution of the MSE and KS distance of g^αξ with respect to α on the real data.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 9: Optimal solution of (P′)
Figure 10: ξ− optimal solution
Figure 11: Empirical CDF of the predictions on the Crime before and after enforcing DP-tails fairness over 20 runs. The parameters are set (arbitrary) to α=0.2 , p=0.4 .
Figure 12: Empirical CDF of the predictions on the California Housing before and after enforcing DP-tails fairness over 20 runs. The parameters are set (arbitrary) to α=1.5 , p=0.4 .
Figure 13: Empirical CDF of the predictions on the Law school before and after enforcing DP-tails fairness over 20 runs. The parameters are set (arbitrary) to α=0.5 , p=0.4 .