2020/11/13 by Evgenii Chzhen, Chzhen, Evgenii, Nicolas Schreuder +1
Mathematics · Social Sciences · #Advanced Causal Inference Techniques #Artificial Intelligence (cs.AI) #Ethics and Social Impacts of AI #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Qualitative Comparative Analysis Research
paper · pdf · doi:10.48550/arxiv.2011.07158
openalex publication_date 2020/11/13 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
Let (X, S, Y) ∈ ℝp × \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 (f(X) | S = 1) amp;\stackreld= (f(X) | S = 2) and Equal Group-Wise Risks 𝔼[(f^*(X) - f(X))2 | S = 1] = 𝔼[(f^*(X) - f(X))2 | S = 2]. 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.