在不区分群体的框架下，实现回归与分类公平性的统一解法。
Demographic parity in regression and classification within the unawareness framework
- 通过最优传输构建公平回归函数，满足群体平等约束。
- 发现分类与回归的最优解在决策集嵌套时可相互转化。
- 适用于需要消除群体差异的公平机器学习场景。
本文研究在不区分群体的框架下，基于人口统计均等性约束的公平回归理论基础，扩展了允许差别对待情形下的已有结果。我们旨在最小化二次损失时刻画最优公平回归函数。结果表明，该函数由具有最优传输成本的质心问题的解给出。此外，我们探讨了最优公平代价敏感分类与最优公平回归之间的联系。证明了分类器决策集的嵌套性是建立分类与回归之间某种等价关系的充要条件。在该嵌套性假设下，最优分类器可通过阈值化最优公平回归函数得到；反之，最优公平回归函数由一系列代价敏感分类器所刻画。
原文摘要 · Abstract (English)
This paper explores the theoretical foundations of fair regression under the constraint of demographic parity within the unawareness framework, where disparate treatment is prohibited, extending existing results where such treatment is permitted. Specifically, we aim to characterize the optimal fair regression function when minimizing the quadratic loss. Our results reveal that this function is given by the solution to a barycenter problem with optimal transport costs. Additionally, we study the connection between optimal fair cost-sensitive classification, and optimal fair regression. We demonstrate that nestedness of the decision sets of the classifiers is both necessary and sufficient to establish a form of equivalence between classification and regression. Under this nestedness assumption, the optimal classifiers can be derived by applying thresholds to the optimal fair regression function; conversely, the optimal fair regression function is characterized by the family of cost-sensitive classifiers.
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