arXiv：cs.LG· Agathe Fernandes Machado, Charlotte Jamotton, Arthur Charpentier·· 5 小时前
多敏感属性分布公平性：联合 Wasserstein 审计与 Shapley 归因
Multi-Sensitive Distributional Fairness: Joint Wasserstein Audits and Shapley Allocation
AI 导读
研究提出多敏感属性下的分布公平性审计框架，用一维 Wasserstein 几何刻画实值评分的联合人口统计平价。该方法通过全单元格条件分位数函数构造 Hilbert 空间随机变量，其方差即为联合差异，并用 Shapley 值实现无需排序的敏感属性归因；在敏感属性独立时退化为 Hoeffding-ANOVA 分解，在相关时则可揭示边际审计掩盖的抑制与冗余效应。
正文
Abstract:Fairness audits with several sensitive attributes are often performed one coordinate at a time. This can miss purely intersectional disparities: a score may be independent of each sensitive coordinate while depending on their joint profile. We study distributional demographic parity for a real-valued score using one-dimensional Wasserstein geometry. We distinguish two complementary constructions. Conditional and sequential audits characterize joint parity through their zero sets, but their positive values do not generally decompose a fixed joint Wasserstein disparity. By contrast, full-cell conditional quantile functions define a Hilbert-valued random variable whose variance is the joint disparity. Conditional expectations of this quantile process induce a monotone information game: every reveal order yields an exact martingale decomposition of the same joint disparity, while Shapley values provide an order-free attribution across sensitive attributes. Under independent sensitive attributes, the game reduces to a Hoeffding-ANOVA decomposition and Shapley splits each interaction energy equally among its members; under dependence, orthogonality is lost and explicit formulas reveal suppression and redundancy effects that marginal audits can hide. We give fixed-grid estimators and permutation calibration, and illustrate the framework on synthetic examples and ACSIncome. The resulting framework separates three questions that are often conflated: whether joint distributional parity holds, how a fixed joint disparity decomposes along an information path, and how that disparity can be attributed across sensitive coordinates without privileging an ordering.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Methodology (stat.ME) |
| Cite as: | arXiv:2610.19252 [stat.ML] |
| (or arXiv:2610.19252v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.19252 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Arthur Charpentier [view email]
[v1]
Tue, 13 Oct 2026 22:13:30 UTC (143 KB)
来源：arXiv：cs.LG · arxiv.org