Fairness guarantee in multi-class classification

Algorithmic Fairness is an established area of machine learning, willing to reduce the influence of biases in the data. Yet, despite its wide range of applications, very few works consider the multi-class classification setting from the fairness perspective. We extend both definitions of exact and approximate fairness in the case of Demographic Parity to multi-class classification. We specify the corresponding expressions of the optimal fair classifiers. This suggests a plug-in data-driven procedure, for which we establish theoretical guarantees. The enhanced estimator is proved to mimic the behavior of the optimal rule both in terms of fairness and risk. Notably, fairness guarantees are distribution-free. The approach is evaluated on both synthetic and real datasets and turns out to be very effective in decision making with a preset level of unfairness. In addition, our method is competitive with the state-of-the-art in-processing fairlearn in the specific binary classification setting.