通过最优传输方法实现因果公平回归，理论保证预测偏差随样本量衰减。
Counterfactually Fair Regression via Optimal Transport
- 基于潜变量重采样定义公平性，构造最优公平回归器的闭式表达
- 在有限样本下证明不公平度以~O(n^{-1/3})速率下降，风险界匹配该速率
- 适用于需要可解释公平性的机器学习场景，尤其关注算法公平性研究者
我们研究学习因果公平回归器的问题。采用因果不确定性视角，将反事实公平性定义为在重采样噪声下的性质。重点在于为一种新的后处理估计器提供理论公平性保证。首先证明反事实公平性等价于在潜变量条件下满足人口均等性，从而通过巴氏量化映射获得最优公平回归器的闭式表达。为处理连续潜变量，提出离散化后处理方法。在弱正则性假设下，证明了估计器的高概率有限样本公平性保证，不公平度以~O(n^{-1/3})速率衰减，并建立同阶风险界~O(n^{-1/3})。还给出了几乎公平预测超额风险的匹配下界。最后将结果扩展至松弛型反事实公平设置。在真实与合成数据上验证了方法的有效性。
原文摘要 · Abstract (English)
We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new post-processing estimator. We begin by showing that counterfactual fairness is equivalent to satisfying demographic parity conditional on the latent variable. This allows us to provide a closed-form expression of the optimal fair regressor via a barycentric quantile map. In order to handle continuous latent variables, we propose a discretized post-processing method. Then, under mild regularity assumptions, we prove high-probability finite-sample fairness guarantees for our estimator, providing an unfairness decay at rate $\tilde O(n^{-1/3})$, and establishing a matching risk bound of order $\tilde O(n^{-1/3})$. We provide a matching lower bound on the excess risk of almost fair predictions. Finally, we extend our results to the setting of relaxed counterfactual fairness. We validate our approach on real-world and synthetic data.
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