Supervised Algorithmic Fairness in Distribution Shifts: A Survey

Fairness in machine learning has emerged as a crucial consideration in real-world applications, particularly in high-stakes scenarios such as hiring, lending, and criminal justice where biased algorithms can perpetuate and worsen inequalities. Fairness aims for equitable treatment of individuals regardless of sensitive characteristics (e.g., race, gender), mitigating discrimination and promoting equal opportunities in model outcomes. Achieving fairness is challenging under distribution shifts: models trained on source distributions may not generalize to target distributions, potentially exacerbating biases and undermining fairness objectives. Addressing these challenges is essential for responsible and ethical deployment of machine learning systems.

The survey reviews supervised algorithmic fairness under distribution shifts, formalizing fairness notions (group, individual, counterfactual) and a general learning objective that balances utility and fairness constraints. It delineates key types of shifts: covariate, label, concept, demographic, dependence, and hybrid combinations, analyzing how each can degrade fairness generalization. The paper categorizes methods into six families: feature disentanglement (often VAE/autoencoder-based), data augmentation (including generative models and combined with disentanglement), causal inference (SCMs, do-operator interventions, counterfactual generation), reweighting (instance/feature weights to approximate target distributions or decouple Y–Z correlations), robust optimization (DRO with uncertainty sets such as Wasserstein balls), and regularization-based approaches (adversarial decorrelation, distribution alignment via MMD). It compiles commonly used datasets (e.g., UCI Adult, COMPAS, NYSF, CMNIST/variants, Waterbirds, FairFace, UTKFace, BOLD, graph datasets) and summarizes fairness evaluation metrics across group fairness (ΔDP, ΔEO, ΔEOP), individual fairness (consistency), and counterfactual fairness (TCE, CE). The survey also situates related fields, including unsupervised fairness under distribution shifts and fairness-aware outlier detection.

The survey provides a formal framework for supervised fairness under distribution shifts. It defines domains as joint distributions P(X, Z, Y), datasets sampled i.i.d. from source domains, and a classifier f_θ trained to jointly minimize prediction error while constraining dependence between predictions and sensitive attributes via a fairness function g with threshold ε. It presents Problem 1: learning a fair classifier from multiple source domains that generalizes to distinct target domains under shifts, optimizing expected loss with fairness constraints. The paper then classifies distribution shifts impacting fairness: covariate (P_X changes), label (P_Y changes), concept (P_{Y|X} changes), demographic (P_Z changes), dependence (P_{Y|Z} or P_{Z|Y} changes), and hybrid combinations. It discusses space changes (X, Y, Z) across domains (e.g., new labels/sensitive attributes) versus proportional changes without space alterations. Six methodological approaches are detailed:

• Feature disentanglement: learn representations R = h(X) that preserve semantics unrelated to Z, often via VAE/autoencoder structures; high interpretability but challenging to assess disentanglement quality.
• Data augmentation: generate transformed or synthetic samples (including GAN-based generators ensuring domain-invariant conditional distributions) and combine with disentanglement to sample domain-specific/sensitive factors with decoders.
• Causal inference: use SCMs and do-operator interventions on X, Z, Y to generate counterfactuals and analyze causal paths contributing to unfairness; evaluate training sample influence and adaptation speed under changing distributions.
• Reweighting: pre-processing to adjust instance/feature weights to better reflect target distributions or decouple Y–Z correlations, followed by in-processing equal weighting within (y, z)-classes.
• Robust optimization: DRO frameworks minimizing worst-case loss over uncertainty sets near the empirical distribution (e.g., Wasserstein balls), sometimes integrating fairness constraints into both min/max problems.
• Regularization-based approaches: adversarial regularization to reduce correlation between representations R and sensitive attributes Z, and distribution alignment (e.g., MMD) to transfer fairness across domains by aligning P_Z and domain label distributions. Other methods include post-processing decision boundary adjustment for streaming/online concept drift and Seldonian-style frameworks to guarantee fairness under demographic shift.

• Distribution shifts (covariate, label, concept, demographic, dependence, hybrid) directly impact fairness generalization; concept shift is particularly challenging due to changes in P_{Y|X} and induced changes in P_{Y|Z}.
• Handling dependence shift is straightforward if correlation is greater in the source than target; otherwise fairness may fail to generalize.
• Six common methodological families recur across the literature: feature disentanglement, data augmentation, causal inference, reweighting, robust optimization, and regularization-based approaches, each with distinct advantages and trade-offs.
• Publicly available datasets and benchmarks span tabular (e.g., UCI Adult: 48,842 samples; COMPAS: 6,167), image (CMNIST/rcMNIST/CCMNIST, Waterbirds, FairFace, UTKFace), text (BOLD), and graph (Pokecs, Bail-Bs, Credit-Cs) domains, enabling empirical study of different shift types.
• Standard fairness metrics used for evaluation include ΔDP, ΔEO, ΔEOP for group fairness; consistency for individual fairness; and TCE/CE for counterfactual fairness.
• The survey highlights practical considerations such as space changes (new labels/sensitive attributes) and the interplay of causal structures (Z → X, Z → Y, X → Y) affecting fairness under shift.

By formalizing the supervised fairness objective under distribution shifts and systematically categorizing both the shifts and mitigation strategies, the survey addresses the central question of how to maintain equitable model behavior when deployment conditions change. The synthesis clarifies when and why fairness degrades (e.g., concept and dependence shifts) and maps established tools—disentanglement, augmentation, causal modeling, reweighting, DRO, and regularization—to specific shift scenarios. The curated datasets and metrics facilitate reproducible empirical evaluation. The discussion underscores the importance of causal reasoning for diagnosing unfairness pathways, robust optimization for worst-case protection, and representation learning for reducing sensitive attribute leakage. These insights support the design of models that balance utility and fairness in dynamic, real-world environments.

The survey compiles and analyzes diverse distribution shifts that undermine fairness generalization, reviews methods spanning six major approaches to mitigate unfairness across source-to-target transitions, and catalogs datasets and evaluation metrics used in empirical studies. It identifies open challenges, including fairness under conditional shift and fairness in out-of-distribution detection, and suggests future directions that integrate causal analysis, robust optimization, and representation learning to better guarantee fairness beyond training distributions.

The survey narrows scope to supervised learning and classification tasks, focusing primarily on fairness under distribution shifts rather than broader settings (e.g., regression). It synthesizes existing literature without presenting new empirical benchmarks. Assessing the quality of feature disentanglement remains challenging, and some shift scenarios (e.g., conditional shift) are identified as promising but are not extensively covered.