  Recent studies showed that datasets used in fairness-aware machine learning
for multiple protected attributes (referred to as multi-discrimination
hereafter) are often imbalanced. The class-imbalance problem is more severe for
the often underrepresented protected group (e.g. female, non-white, etc.) in
the critical minority class. Still, existing methods focus only on the overall
error-discrimination trade-off, ignoring the imbalance problem, thus amplifying
the prevalent bias in the minority classes. Therefore, solutions are needed to
solve the combined problem of multi-discrimination and class-imbalance. To this
end, we introduce a new fairness measure, Multi-Max Mistreatment (MMM), which
considers both (multi-attribute) protected group and class membership of
instances to measure discrimination. To solve the combined problem, we propose
a boosting approach that incorporates MMM-costs in the distribution update and
post-training selects the optimal trade-off among accurate, balanced, and fair
solutions. The experimental results show the superiority of our approach
against state-of-the-art methods in producing the best balanced performance
across groups and classes and the best accuracy for the protected groups in the
minority class.
