Demographic Parity Tails for Regression

Abstract

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 (13)

• Figure 1: Illustration for $t\mapsto Q^*_s(t)$ for some $s\in \mathcal{S}$ in the case where $\alpha\leq \sum\limits_{s\in\mathcal{S}}p_sQ_{f^*|s}(p)$ (red curve).
• Figure 2: Illustration for $t\mapsto Q^{\xi}_s(t)$ on $(p,1]$ in the case where $\alpha > \sum\limits_{s\in\mathcal{S}}p_sQ_{f^*|s}(p)$ (red curve).
• Figure 3: Histogram of predictions on synthetic data before (left) and after (right) enforcing $(\alpha,p)$-DP-tails fairness. The constraint parameters are set (arbitrary) to $\alpha=0$, $p=0.5$
• 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 $\alpha=0$, $p=0.5$; plot (c): $\alpha=0$ and $p$ minimizes \ref{['eq:OptimProblemP']}.
• Figure 5: Evolution of the tail unfairness of $\hat{g}_{\alpha,p}^{\xi}$ with respect to the size $N$ of the unlabeled dataset on the synthetic data.

Theorems & Definitions (26)

• Definition 2.2: Demographic Parity Tails
• Definition 2.3: $2-$Wasserstein distance
• Theorem 2.4
• Theorem 2.5: Optimal DP-tails fair prediction
• Remark 2.6
• Remark 2.7
• Theorem 3.1: DP-tails fairness guarantees
• Theorem 3.5
• Definition 4.1: Relaxed DP-Tails
• Lemma 1.1