Impact of Data Distribution on Fairness Guarantees in Equitable Deep Learning

TL;DR

The paper addresses fairness guarantees in equitable deep learning under heterogeneous data distributions, with high-stakes medical-imaging and facial-recognition applications. It builds a formal framework that minimizes the maximum group-loss difference, defined as $\Delta(f) = \max_{i,j} |L_i(f) - L_j(f)|$, and proves bounds on fairness error, convergence, and group-specific risks under distributional assumptions. Empirical validation on FairVision, CheXpert, HAM10000, and FairFace shows that distribution shifts across groups predict fairness gaps, with disparities most pronounced for racial groups. The results provide a theoretical foundation and practical guidance for designing more equitable AI systems in high-stakes diagnostics and related domains.

Abstract

We present a comprehensive theoretical framework analyzing the relationship between data distributions and fairness guarantees in equitable deep learning. Our work establishes novel theoretical bounds that explicitly account for data distribution heterogeneity across demographic groups, while introducing a formal analysis framework that minimizes expected loss differences across these groups. We derive comprehensive theoretical bounds for fairness errors and convergence rates, and characterize how distributional differences between groups affect the fundamental trade-off between fairness and accuracy. Through extensive experiments on diverse datasets, including FairVision (ophthalmology), CheXpert (chest X-rays), HAM10000 (dermatology), and FairFace (facial recognition), we validate our theoretical findings and demonstrate that differences in feature distributions across demographic groups significantly impact model fairness, with performance disparities particularly pronounced in racial categories. The theoretical bounds we derive crroborate these empirical observations, providing insights into the fundamental limits of achieving fairness in deep learning models when faced with heterogeneous data distributions. This work advances our understanding of fairness in AI-based diagnosis systems and provides a theoretical foundation for developing more equitable algorithms. The code for analysis is publicly available via \url{https://github.com/Harvard-Ophthalmology-AI-Lab/fairness_guarantees}.

Figures (6)

• Figure 1: Feature distribution and AUC comparison of ViT and EfficientNet for AMD detection across three demographic attributes, including Race, Gender, and Ethnicity, on FairVision dataset
• Figure 2: Feature distribution and AUC comparison of ViT and EfficientNet for DR detection across three demographic attributes, including Race, Gender, and Ethnicity, on FairVision dataset
• Figure 3: Feature distribution and AUC comparison of ViT and EfficientNet for Glaucoma (GL) detection across three demographic attributes, including Race, Gender, and Ethnicity, on FairVision dataset.
• Figure 4: Feature distribution and AUC comparison of EfficientNet for Pleural Effusion (PE) detection across two demographic attributes, including Race and Gender, on Chexpert dataset.
• Figure 5: Feature distribution and AUC comparison of EfficientNet for Skin Cancer (SC) detection across two demographic attributes, including Gender and Age, on HAM10000 dataset.

Theorems & Definitions (28)

• Definition 3.1: Fairness Problem
• Theorem 3.2: Connection with Conventional Fairness
• proof
• Theorem 3.4: Fairness Error Bound
• proof
• Definition 3.5: $\epsilon$-optimal Solution
• Theorem 3.7: Algorithm Complexity of Fairness Problem
• proof
• Lemma 3.8: Uniform Convergence Bound for Fairness Problem
• Lemma 3.9: Symmetrization