In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, and optimal transport. We extend "Knothe's rearrangement" and "triangular transport" to probabilistic graphical models, and use this counterfactual approach, referred to as sequential transport, to discuss fairness at the individual level. After establishing the theoretical foundations of the proposed method, we demonstrate its application through numerical experiments on both synthetic and real datasets.

Machine learning (ML) models are increasingly used in high-stakes decisions, such as insurance pricing and pretrial detention, but often reproduce or amplify biases present in data. To mitigate discrimination, optimal transport (OT) offers a principled way to transform unfair model predictions into fair ones while minimizing performance loss. Moreover, uncertainty-based methods like calibration help assess fairness across sensitive groups, while uncertainty attribution helps identify sources of bias. This research aims to address algorithmic fairness challenges by developing evaluation and mitigation techniques with theoretical guarantees from OT, easily deployable in practice, while integrating fairness into the broader framework of trustworthy AI—enhancing calibration and uncertainty attribution methods to ensure ethical use of ML models by transparency and reliability.

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 or sequential transport 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 the Euclidean space. We demonstrate the applicability and effectiveness of this approach through an illustration on real-world data, and discuss limitations.