Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport
This addresses a significant bottleneck in practical fairness applications with real datasets, though it is incremental as it builds on existing optimal transport methods.
The paper tackles the challenge of transporting categorical variables for counterfactual fairness analysis by converting them into compositional data and transporting within a probabilistic simplex, demonstrating applicability on real-world data.
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.