On Thursday 12th, I will attend the Mathematical Foundations of AI day, organized by the DATAIA Institute and SCAI (Sorbonne Center for Artificial Intelligence), in association with several scientific societies (namely, the Fondation Mathématique Jacques Hadamard (FMJH), the Fondation Sciences Mathématiques de Paris-FSMP, the MALIA group of the Société Française de Statistique and the Société Savante Francophone d’Apprentissage Machine (SSFAM)).

Slides are now online.

In this talk, we present two complementary approaches to addressing fairness in algorithmic decision-making through the lens of counterfactual reasoning and optimal transport, both in individual and group fairness. First, we introduce a novel method that links two existing counterfactual approaches: causal graph-based adaptations (Plečko and Meinshausen, 2020) and optimal transport (De Lara et al., 2024). By extending “Knothe’s rearrangement” (Bonnotte, 2013) and “triangular transport” (Zech and Marzouk, 2022) to probabilistic graphical models, we propose a new group framework, termed sequential transport, which we apply to the problem of individual fairness. Theoretical foundations are established, followed by numerical demonstrations on synthetic and real datasets. Building on this, we extend the discussion to algorithmic fairness in the presence of multiple sensitive attributes. While traditional fairness frameworks focus on eliminating bias with respect to a single sensitive variable, their effectiveness diminishes with multiple sensitive characteristics. To address this, we propose a sequential fairness framework based on multi-marginal Wasserstein barycenters, generalizing Strong Demographic Parity to handle multiple sensitive features. Our method provides a closed-form solution for the optimal, sequentially fair predictor, enabling interpretation of correlations between sensitive attributes. Furthermore, we introduce an approximate fairness framework that balances risk and unfairness, allowing for prioritization of fairness across specific attributes. Both approaches are supported by comprehensive numerical experiments on synthetic and real-world datasets, showcasing the practical efficacy of these methods in promoting fair decision-making. Together, they provide a robust framework for addressing fairness in complex, multi-attribute settings while preserving interpretability and flexibility.

References are given below

1. we will discuss further counterfactual fairness, initiated in Optimal Transport for Counterfactual Estimation: A Method for Causal Inference, and the more recent paper Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness 
2. we will discuss Wasserstein barycenters with multiple sensistive attributes, A Sequentially Fair Mechanism for Multiple Sensitive Attributes

[added on Sept 13th] Thanks Stéphane Loisel (on the right) for this nice picture with Gilbert Saporta.