On Demographic Group Fairness Guarantees in Deep Learning

We present a theoretical framework analyzing the relationship between data distributions and fairness guarantees in equitable deep learning. We establish novel bounds that account for distribution heterogeneity across demographic groups, deriving fairness error and convergence rate bounds that characterize how distributional differences affect the fairness-accuracy trade-off. Extensive experiments across diverse modalities, including FairVision, CheXpert, HAM10000, FairFace, ACS Income, and CivilComments-WILDS, validate our theoretical findings, demonstrating that feature distribution differences across demographic groups significantly impact model fairness, with disparities particularly pronounced in racial categories. Motivated by these insights, we propose Fairness-Aware Regularization (FAR), a practical training objective that minimizes inter-group discrepancies in feature centroids and covariances. FAR consistently improves overall AUC, ES-AUC, and subgroup performance across all datasets. Our work advances the theoretical understanding of fairness in AI systems and provides a foundation for developing more equitable algorithms. The code for analysis is publicly available at https://github.com/Harvard-AI-and-Robotics-Lab/FairnessGuarantee.

💡 Research Summary

The paper presents a comprehensive theoretical and empirical investigation of how demographic group‑specific data distribution heterogeneity influences fairness guarantees in deep learning models. The authors formalize fairness as the minimization of the maximum difference in expected loss across all protected groups and derive a novel decomposition of the fairness error (Δ) into three components: an irreducible term stemming from inherent label noise, a statistical term reflecting finite‑sample estimation error, and an optimization term capturing algorithmic approximation. Under standard Lipschitz and bounded‑loss assumptions, they prove that Δ converges at a rate of O(1/√m) with respect to the total sample size m, offering a tighter bound than conventional generalization analyses that ignore group‑wise disparities.

A central theoretical contribution is the explicit linkage between a group’s excess risk and its feature distribution shift relative to other groups. By employing the 1‑Wasserstein distance for mean differences and the Frobenius norm for covariance differences, the authors show that the expected loss for any group i satisfies
R_i(f) ≤ R_pop(f) + α‖μ_i−μ_j‖₂ + β‖Σ_i−Σ_j‖_F,
where μ_i and Σ_i denote the mean and covariance of the learned feature representation for group i, and α, β are constants derived from the loss’s Lipschitz constant. This result (Theorems 3.17, 3.19) quantifies how measurable distributional discrepancies directly upper‑bound fairness gaps, especially pronounced for attributes such as race where mean and covariance shifts are large.

Motivated by these insights, the authors propose Fairness‑Aware Regularization (FAR). FAR augments the standard empirical risk minimization objective with a regularization term R_fair that penalizes both inter‑group centroid distances and inter‑group covariance differences:
R_fair = Σ_{i<j}