OPTIMIZATION HIERARCHY FOR FAIR STATISTICAL DECISION PROBLEMS

• 成果类型: Article
• 署名作者: Aswani, Anil; Olfat, Matt
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2217
• 发表日期: 2022
• 页码: 3144-3173
• 关键词: support; dependence

摘要

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 spe-cialized to one model context and based on ad hoc arguments, which makes it difficult to perform theoretical analysis. This paper develops an optimization hierarchy, which is a sequence of optimization problems with an increasing number of constraints, for fair statistical decision problems. Because our hier-archy 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 classifica-tion. 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 nu-merical 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 ef-fectiveness of our hierarchy using several data sets, and we use our hierarchy to fairly perform automated dosing of morphine.