  Machine Learning models are increasingly used for decision making, in
particular in high-stakes applications such as credit scoring, medicine or
recidivism prediction. However, there are growing concerns about these models
with respect to their lack of interpretability and the undesirable biases they
can generate or reproduce. While the concepts of interpretability and fairness
have been extensively studied by the scientific community in recent years, few
works have tackled the general multi-class classification problem under
fairness constraints, and none of them proposes to generate fair and
interpretable models for multi-class classification. In this paper, we use
Mixed-Integer Linear Programming (MILP) techniques to produce inherently
interpretable scoring systems under sparsity and fairness constraints, for the
general multi-class classification setup. Our work generalizes the SLIM
(Supersparse Linear Integer Models) framework that was proposed by Rudin and
Ustun to learn optimal scoring systems for binary classification. The use of
MILP techniques allows for an easy integration of diverse operational
constraints (such as, but not restricted to, fairness or sparsity), but also
for the building of certifiably optimal models (or sub-optimal models with
bounded optimality gap).
