Bounding and Approximating Intersectional Fairness through Marginal Fairness
This work addresses the challenge of measuring intersectional fairness in machine learning, which is critical for preventing discrimination in subgroups but often infeasible due to exponential complexity, offering a practical solution for researchers and practitioners in fairness-aware AI.
The paper tackles the problem of ensuring intersectional fairness across multiple protected attributes by analyzing the relationship between marginal and intersectional fairness, proving high-probability bounds that are computable from marginal fairness and statistical quantities, and demonstrating improved approximations and bounds on real and synthetic datasets.
Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that ensuring \emph{marginal fairness} for every dimension independently is not sufficient in general. Due to the exponential number of subgroups, however, directly measuring intersectional fairness from data is impossible. In this paper, our primary goal is to understand in detail the relationship between marginal and intersectional fairness through statistical analysis. We first identify a set of sufficient conditions under which an exact relationship can be obtained. Then, we prove bounds (easily computable through marginal fairness and other meaningful statistical quantities) in high-probability on intersectional fairness in the general case. Beyond their descriptive value, we show that these theoretical bounds can be leveraged to derive a heuristic improving the approximation and bounds of intersectional fairness by choosing, in a relevant manner, protected attributes for which we describe intersectional subgroups. Finally, we test the performance of our approximations and bounds on real and synthetic data-sets.