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

Agathe Fernandes Machado, Arthur Charpentier and Ewen Gallic
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Agathe Fernandes Machado: UQAM - Université du Québec à Montréal = University of Québec in Montréal
Arthur Charpentier: UQAM - Université du Québec à Montréal = University of Québec in Montréal
Ewen Gallic: AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, CNRS – Université de Montréal CRM – CNRS

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Abstract: Recently, optimal transport-based approaches have gained attention for deriving counterfactuals, e.g., to quantify algorithmic discrimination. However, in the general multivariate setting, these methods are often opaque and difficult to interpret. To address this, alternative methodologies have been proposed, using causal graphs combined with iterative quantile regressions (Plečko and Meinshausen (2020)) or sequential transport (Fernandes Machado et al. (2025)) to examine fairness at the individual level, often referred to as ``counterfactual fairness.'' Despite these advancements, transporting categorical variables remains a significant challenge in practical applications with real datasets. In this paper, we propose a novel approach to address this issue. Our method involves (1) converting categorical variables into compositional data and (2) transporting these compositions within the probabilistic simplex of $\mathbb{R}^d$. We demonstrate the applicability and effectiveness of this approach through an illustration on real-world data, and discuss limitations.

Keywords: Machine Learning (cs.LG); Methodology (stat.ME); FOS: Computer and information sciences (search for similar items in EconPapers)
Date: 2025-05-26
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-05085147

DOI: 10.48550/arXiv.2501.15549

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