A Canonical Data Transformation for Achieving Inter- and Within-Group Fairness

Increases in the deployment of machine learning algorithms for applications that deal with sensitive data have brought attention to the issue of fairness in machine learning. Many works have been devoted to applications that require different demographic groups to be treated fairly. However, algorithms that aim to satisfy inter-group fairness (also called group fairness) may inadvertently treat individuals within the same demographic group unfairly. To address this issue, this article introduces a formal definition of within-group fairness that maintains fairness among individuals from within the same group. A pre-processing framework is proposed to meet both inter- and within-group fairness criteria with little compromise in performance. The framework maps the feature vectors of members from different groups to an inter-group fair canonical domain before feeding them into a scoring function. The mapping is constructed to preserve the relative relationship between the scores obtained from the unprocessed feature vectors of individuals from the same demographic group, guaranteeing within-group fairness. This framework has been applied to the Adult, COMPAS risk assessment, and Law School datasets, and its performance is demonstrated and compared with two regularization-based methods in achieving inter-group and within-group fairness.