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

arXiv: https://arxiv.org/abs/2011.07158 · HTML: https://mlsanity.com/paper/2011.07158/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Regression under demographic parity constraints via unlabeled post-processing](https://mlsanity.com/paper/2407.15453/) (2024)
- [Demographic parity in regression and classification within the unawareness framework](https://mlsanity.com/paper/2409.02471/) (2024)

## Abstract (arXiv)

Let (X, S, Y) ∈ ℝp × 1, 2 × ℝ be a triplet following some joint distribution mathbbP 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) = mathbbE[Y | X = x]. We provide a non-trivial example of a prediction x → f(x) which satisfies two common group-fairness notions: Demographic Parity beginalign (f(X) | S = 1) &stackreld= (f(X) | S = 2) endalign and Equal Group-Wise Risks beginalign mathbbE[(f^*(X) - f(X))2 | S = 1] = mathbbE[(f^*(X) - f(X))2 | S = 2]. endalign 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.