  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, we introduce a formal definition of within-group fairness that maintains
fairness among individuals from within the same group. We propose a
pre-processing framework to meet both inter- and within-group fairness criteria
with little compromise in accuracy. 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. We apply this framework to the COMPAS risk assessment
and Law School datasets and compare its performance in achieving inter-group
and within-group fairness to two regularization-based methods.
