论文标题
与Wasserstein Barycenters的公平回归
Fair Regression with Wasserstein Barycenters
论文作者
论文摘要
我们研究学习满足人口统计学限制的实现功能的问题。它要求预测输出的分布独立于敏感属性。我们认为敏感属性可用于预测。我们建立了公平回归与最佳运输理论之间的联系，基于我们为最佳公平预测变量得出近距离表达式。具体而言，我们表明，该最佳的分布是敏感组标准回归函数引起的分布的Wasserstein Barycenter。该结果提供了对最佳公平预测的直观解释，并提出了一种简单的后处理算法，以实现公平性。我们为此程序建立了无风险和无分配公平性保证。数值实验表明，我们的方法在学习公平模型中非常有效，错误率相对增加，远低于公平性相对增益。
We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the sensitive attribute is available for prediction. We establish a connection between fair regression and optimal transport theory, based on which we derive a close form expression for the optimal fair predictor. Specifically, we show that the distribution of this optimum is the Wasserstein barycenter of the distributions induced by the standard regression function on the sensitive groups. This result offers an intuitive interpretation of the optimal fair prediction and suggests a simple post-processing algorithm to achieve fairness. We establish risk and distribution-free fairness guarantees for this procedure. Numerical experiments indicate that our method is very effective in learning fair models, with a relative increase in error rate that is inferior to the relative gain in fairness.
