Applications that deal with sensitive information may have restrictions placed on the data available to a machine learning (ML) classifier. For example, in some applications, a classifier may not have direct access to sensitive attributes, affecting its ability to produce accurate and fair decisions. This paper proposes a framework that models the trade-off between accuracy and fairness under four practical scenarios that dictate the type of data available for analysis. Prior works examine this trade-off by analyzing the outputs of a scoring function that has been trained to implicitly learn the underlying distribution of the feature vector, class label, and sensitive attribute of a dataset. In contrast, our framework directly analyzes the behavior of the optimal Bayesian classifier on this underlying distribution by constructing a discrete approximation it from the dataset itself. This approach enables us to formulate multiple convex optimization problems, which allow us to answer the question: How is the accuracy of a Bayesian classifier affected in different data restricting scenarios when constrained to be fair? Analysis is performed on a set of fairness definitions that include group and individual fairness. Experiments on three datasets demonstrate the utility of the proposed framework as a tool for quantifying the trade-offs among different fairness notions and their distributional dependencies.

翻译：涉及敏感信息的应用可能对机器学习分类器可用的数据施加限制。例如，在某些应用中，分类器可能无法直接访问敏感属性，从而影响其产生准确且公平决策的能力。本文提出一个框架，在四种实际场景下模拟准确性与公平性之间的权衡，这些场景取决于可供分析的数据类型。先前的研究通过分析已训练评分函数的输出来考察这一权衡，该评分函数隐式学习了特征向量、类别标签和数据集敏感属性的底层分布。相比之下，我们的框架通过从数据集本身构建其离散近似，直接分析最优贝叶斯分类器在该底层分布上的行为。该方法使我们能够构建多个凸优化问题，从而回答以下问题：当需满足公平性约束时，不同数据限制场景下贝叶斯分类器的准确性如何受到影响？分析基于一组公平性定义，包括群体公平性和个体公平性。在三个数据集上的实验表明，所提出的框架可作为量化不同公平性概念及其分布依赖关系之间权衡的有效工具。