Agathe Fernandes Machado

Algorithmic fairness refers to the set of principles and techniques aimed at ensuring that the decisions produced by an algorithm are fair and non-discriminatory toward all users, regardless of personal characteristics such as gender, ethnicity, or other so-called sensitive attributes. Its assessment can be carried out at multiple levels: on the one hand, at the group level, by comparing a model’s predictions across different groups defined by sensitive variables; and on the other hand, at the individual level, by focusing on a specific individual from a minority group and asking counterfactual questions such as: “What would this woman’s salary be if she were a man?” To evaluate algorithmic fairness at the individual level, we adopt the notion of Counterfactual Fairness proposed by Kusner et al. (2017). This approach relies on the mutatis mutandis principle, in contrast to the ceteris paribus principle: rather than checking whether a model’s prediction for an individual remains unchanged when only the sensitive attribute is modified while keeping all other explanatory variables constant, we ask whether the prediction remains the same when only the variables not causally influenced by the sensitive attribute are held constant. The definition of Counterfactual Fairness relies on Pearl’s (2009) causal inference framework and involves computing an individual’s counterfactual in which the sensitive attribute is modified, assuming prior knowledge of a causal graph over the model’s explanatory variables. In this study, we link two existing approaches to derive counterfactuals: intervention-based approaches on a causal graph with quantile preservation, as proposed by Plečko et al. (2020), and multivariate optimal transport introduced by Lara et al. (2024). We extend the concepts of “Knothe’s rearrangement” and “triangular transport” to probabilistic graphical models and establish the theoretical foundations of a counterfactual approach, called sequential transport, to discuss individual-level fairness.