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 address this question by extending the definition of Demographic Parity to the multi-class problem while specifying the corresponding expression of the optimal fair classifier. This suggests a plug-in data-driven procedure, for which we establish theoretical guarantees. Specifically, we show that the enhanced estimator mimics the behavior of the optimal rule, both in terms of fairness and risk. Notably, fairness guarantee is distribution-free. We illustrate numerically the quality of our algorithm. The procedure reveals to be much more suitable than an alternative approach enforcing fairness constraints on the score associated to each class. This shows that our method is empirically very effective in fair decision making on both synthetic and real datasets.