Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport

Counterfactual analysis is an essential method in machine learning, policy evaluation, economics and causal inference. It involves reasoning about "what could have happened" under alternative scenarios, providing insights into causality and decision-making effectiveness. An example could be the concept of counterfactual fairness, as introduced by Kusner et al. (2017), that ensures fairness by evaluating how decisions would change under alternative, counterfactual conditions. Counterfactual fairness focuses on mitigating bias by ensuring that sensitive attributes, such as race, gender, or socioeconomic status, do not unfairly influence outcomes. Agathe Fernandes Machado acknowledges that the project leading to this publication has received funding from OBVIA. Arthur Charpentier acknowledges funding from the SCOR Foundation for Science and the National Sciences and Engineering Research Council (NSERC) for funding (RGPIN-2019-07077). Ewen Gallic acknowledges funding from the French government under the "France 2030" investment plan managed by the French National Research Agency (reference: ANR-17-EURE-0020) and from Excellence Initiative of Aix-Marseille University - A*MIDEX.