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

TL;DR

This paper introduces a novel optimal transport method for categorical data by transforming it into compositional data and transporting within the probability simplex, enhancing interpretability in counterfactual analysis.

Contribution

The paper proposes a new approach that converts categorical variables into compositional data and applies transport within the simplex, addressing a key challenge in practical counterfactual fairness applications.

Findings

Effective transportation of categorical variables demonstrated on real data.

Improved interpretability of counterfactuals in categorical settings.

Discussion of limitations and potential extensions.

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 (Ple\v{c}ko 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.