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

Our recent paper, Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport, with Agathe and Ewen is now online

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.

https://freakonometrics.hypotheses.org/files/2025/01/transp2.png

See https://github.com/fer-agathe/transport-simplex for the codes


OpenEdition suggests that you cite this post as follows:
Arthur Charpentier (January 27, 2025). Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport. Freakonometrics. Retrieved February 18, 2025 from https://doi.org/10.58079/136b2


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