A Convex Framework for Fair Regression

The widespread use of machine learning to make consequential decisions about individual citizens (including in domains such as credit, employment, education and criminal sentencing [3, 4, 26, 29]) has been accompanied by increased reports of instances in which the algorithms and models employed can be unfair or discriminatory in a variety of ways [2, 30]. As a result, research on fairness in machine learning and statistics has seen rapid growth in recent years [1, 5-7, 9-11, 13, 14, 18-21, 25, 27], and several mathematical formulations have been proposed as metrics of (un)fairness for a number of different learning frameworks. While much of the attention to date has focused on (binary) classification settings, where standard fairness notions include equal false positive or negative rates across different populations, less attention has been paid to fairness in (linear and logistic) regression settings, where the target and/or predicted values are continuous, and the same value may not occur even twice in the training data. In this work, we introduce a rich family of fairness metrics for regression models that take the form of a fairness regularizer and apply them to the standard loss functions for linear and logistic regression. Since these loss functions and our fairness regularizer are convex, the combined objective functions obtained from our framework are also convex, and thus permit efficient optimization. Furthermore, our family of fairness metrics covers the spectrum from the type of group fairness that is common in classification formulations (where e.g.