Optimization hierarchy for fair statistical decision problems
Optimization hierarchy for fair statistical decision problems
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DOI：
10.1214/22-aos2217
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
A. Aswani;Matt Olfat
中科院分区：
文献类型：
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作者：
A. Aswani;Matt Olfat
由于担心潜在的歧视，数据驱动的决策引起了决策者的密切关注，越来越多的文献开始开发公平的统计技术。然而，这些技术通常专用于一个模型上下文，并基于特定的参数，这使得很难进行理论分析。本文提出了一个公平统计决策问题的优化层次。由于我们的层次结构是基于统计决策问题的框架，这意味着它提供了一个系统的方法来开发和研究假设检验，决策，估计，回归和分类的公平版本。我们使用的洞察力，公平性的定性定义是等同于统计技术的输出和随机变量，测量属性的公平性是理想的统计独立性。我们使用这种见解来构建一个优化层次，本身适合数值计算，我们使用变分分析和随机集理论的工具来证明，这个层次结构的更高层次的一致性，在这个意义上，它渐近地施加这种独立性作为相应的统计决策问题的约束。我们证明了我们的层次结构使用几个数据集的数值有效性，我们的结论是使用我们的层次结构，公平地执行自动给药吗啡。
Data-driven decision-making has drawn scrutiny from policy makers due to fears of potential discrimination, and a growing literature has begun to develop fair statistical techniques. However, these techniques are often specialized to one model context and based on ad-hoc arguments, which makes it difficult to perform theoretical analysis. This paper develops an optimization hierarchy for fair statistical decision problems. Because our hierarchy is based on the framework of statistical decision problems, this means it provides a systematic approach for developing and studying fair versions of hypothesis testing, decision-making, estimation, regression, and classification. We use the insight that qualitative definitions of fairness are equivalent to statistical independence between the output of a statistical technique and a random variable that measures attributes for which fairness is desired. We use this insight to construct an optimization hierarchy that lends itself to numerical computation, and we use tools from variational analysis and random set theory to prove that higher levels of this hierarchy lead to consistency in the sense that it asymptotically imposes this independence as a constraint in corresponding statistical decision problems. We demonstrate numerical effectiveness of our hierarchy using several data sets, and we conclude by using our hierarchy to fairly perform automated dosing of morphine.