An example of prediction which complies with Demographic Parity and equalizes group-wise risks in the context of regression

Abstract

Let (X, S, Y) R^p \1, 2\ R be a triplet following some joint distribution P with feature vector X, sensitive attribute S , and target variable Y. The Bayes optimal prediction f^* which does not produce Disparate Treatment is defined as f^*(x) = E[Y | X = x]. We provide a non-trivial example of a prediction x f(x) which satisfies two common group-fairness notions: Demographic Parity align (f(X) | S = 1) &d= (f(X) | S = 2) align and Equal Group-Wise Risks align E[(f^*(X) - f(X))^2 | S = 1] = E[(f^*(X) - f(X))^2 | S = 2]. align To the best of our knowledge this is the first explicit construction of a non-constant predictor satisfying the above. We discuss several implications of this result on better understanding of mathematical notions of algorithmic fairness.

Tasks

Reproductions