Enhancing Fairness in Multi-Class Classification: A Post-Processing Approach with Linear Programming

In the contemporary landscape of AI and ML applications algorithmic fairness plays an important role. While extensive research has delved into fairness in binary classification and regression scenarios, the exploration of fairness in multi-class classification task has been relatively limited despite its potential usefulness in areas like credit scoring, school and university admission, criminal jurisdiction, etc. Indeed, in all these problems, the predicted label may take more than two values. The credit liability may be estimated as "low", "medium" and "high’"; the risk of recidivism may also have several values; the future performance of a student can be evaluated as a non-binary variable. In this paper, we present a post-processing type algorithm that increases fairness in multi-class classification problems. The core of our approach is a linear programming problem that allows our algorithm to relabel some predictions of the initial classifier in order to improve fairness with a small possible loss in accuracy. We observe decent performance of our algorithm on synthetic and real datasets COMPAS, LOAN, LSAC, ENEM, HSLS. The algorithm's general applicability and positive impact on fairness metrics position it as a valuable tool for mitigating fairness challenges in AI. Notably, our approach exhibits resilience even when confronted with non-optimal initial classifiers, reinforcing its practical utility and adaptability.