Intersectional Fairness via Mixed-Integer Optimization

The deployment of Artificial Intelligence in high-risk domains, such as finance and healthcare, necessitates models that are both fair and transparent. While regulatory frameworks, including the EU's AI Act, mandate bias mitigation, they are deliberately vague about the definition of bias. In line with existing research, we argue that true fairness requires addressing bias at the intersections of protected groups. We propose a unified framework that leverages Mixed-Integer Optimization (MIO) to train intersectionally fair and intrinsically interpretable classifiers. We prove the equivalence of two measures of intersectional fairness (MSD and SPSF) in detecting the most unfair subgroup and empirically demonstrate that our MIO-based algorithm improves performance in finding bias. We train high-performing, interpretable classifiers that bound intersectional bias below an acceptable threshold, offering a robust solution for regulated industries and beyond.

Bias Detection via Maximum Subgroup Discrepancy

Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study a distance of a given dataset, viewed as a distribution, to a given ground-truth reference dataset. However, classical metrics, such as the Total Variation and the Wasserstein distances, are known to have high sample complexities and, therefore, may fail to provide meaningful distinction in many practical scenarios. In this paper, we propose a new notion of distance, the Maximum Subgroup Discrepancy (MSD). In this metric, two distributions are close if, roughly, discrepancies are low for all feature subgroups. While the number of subgroups may be exponential, we show that the sample complexity is linear in the number of features, thus making it feasible for practical applications. Moreover, we provide a practical algorithm for the evaluation of the distance, based on Mixed-integer optimization (MIO). We also note that the proposed distance is easily interpretable, thus providing clearer paths to fixing the biases once they have been identified. It also provides guarantees for all subgroups. Finally, we empirically evaluate, compare with other metrics, and demonstrate the above properties of MSD on real-world datasets.