Intersectional Fairness via Mixed-Integer Optimization

Machine learning models have been shown to exhibit discriminatory outcomes or degraded performance for individuals at the intersection of multiple sensitive attributes, such as race and gender. This stems in part from two interrelated challenges: the lack of principled measures for quantifying bias (potentially intersectional), and insufficient representation of intersectional subgroups in training data. We extend a recent bias mitigation framework to incorporate coverage constraints that enforce sufficient representation across groups, including intersectional subgroups. Since achieving exactly zero bias for all groups may not be data efficient (meaning it may require large amounts of data), our solution trades small approximation errors in bias for greater data efficiency while satisfying coverage constraints. We also formulate bias mitigation as an integer linear program that optimizes over all mitigation strategies, and characterize the price of fairness, the minimum data modification cost, as a function of fairness tolerance. This is essential both for legal compliance, where regulations may mandate specific fairness thresholds, and for data governance, enabling practitioners to make informed trade-offs between bias reduction and data modification (particularly, data purchasing) costs. We evaluate our techniques on publicly available datasets, demonstrating that bias mitigation via our framework preserves predictive accuracy across multiple classifiers, and that coverage constraints, while motivated by statistical considerations, are essential for preserving downstream ML performance.

Hybrid interpretable models combine a transparent component with a black-box model by assigning some examples to the former and deferring the rest to the latter. While this design enables flexible tradeoffs between accuracy and interpretability, it also raises a distinct procedural fairness concern: some demographic groups may systematically receive interpretable decisions, while others are disproportionately routed to a black box. We formalize this issue as Interpretability Coverage Disparity (ICD), a demographic-parity-style measure applied to the routing decision of hybrid interpretable models. Using tools from predictive multiplicity, we study ICD across four hybrid interpretable learning methods, three standard fairness benchmark datasets, and multiple sensitive attributes. Our experiments reveal substantial ICD in intermediate transparency regimes, where both the interpretable and black-box components are actively used. We further show that simple coverage-disparity constraints can significantly reduce ICD in exact hybrid learning methods, with marginal impact on accuracy and sparsity. In several settings, ICD mitigation also improves standard algorithmic fairness metrics. These results show that hybrid interpretable models should be audited not only for predictive fairness, but also for how they allocate interpretability across individuals and groups.

Fairness in machine learning remains challenging due to its ethical complexity, the absence of a universal definition, and the need for context-specific bias metrics. Existing methods still struggle with intersectionality, multiclass settings, and limited flexibility and generality. To address these gaps, we introduce MIFair, a unified framework for bias assessment and mitigation based on mutual information. MIFair provides a flexible metric template and an in-processing mitigation method inspired by the Prejudice Remover, defining group fairness as statistical independence between prediction-derived variables and sensitive attributes. We further strengthen its information-theoretic foundation by establishing equivalences with widely used fairness notions such as independence and separation. MIFair naturally supports intersectionality, complex subgroup structures, and multiclass classification and employs regularization-based training to reduce bias according to the selected metric. Its key advantage is its versatility: it consolidates diverse fairness requirements into a single coherent framework, enabling consistent benchmarking and simplifying practical use. Experiments on real-world tabular and image datasets show that MIFair effectively reduces bias, including previously unaddressed multi-attribute scenarios, while maintaining strong predictive performance across the evaluated settings.