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

2025-01-26

AI Summary

This work addresses the challenge of modeling counterfactual fairness for multivariate categorical data (e.g., gender, race). We propose a novel method integrating compositional data analysis and optimal transport. Specifically, we map categorical variables to the probability simplex—representing them as Dirichlet-distributed compositional data—and define a Wasserstein-type optimal transport metric on this geometric structure. This enables differentiable and interpretable counterfactual inference over discrete variables. Our approach overcomes a key limitation of conventional optimal transport methods, which struggle with non-Euclidean discrete domains, and supports individual-level fairness quantification and attribution analysis. Experiments on multiple real-world datasets demonstrate that our method significantly improves both the plausibility of generated counterfactuals and the accuracy of fairness assessment, while maintaining theoretical rigor and practical interpretability.

Technology Category

• Computer Vision: Bias, Fairness & Privacy
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 (Plev{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.

Problem

• Counterfactual Fairness
• Multivariate Analysis
• Categorical Variables

Innovation

• Categorical Variables Transformation
• Dirichlet Transmission Method
• Counterfactual Fairness Analysis