Directly Optimizing Mean Demographic Parity for Nonlinear Regression
Abstract
We focus on regression settings where the fairness goal is to equalize average predictions across values of a sensitive attribute, a criterion known as mean demographic parity. Directly optimizing this criterion is difficult because it depends on a conditional mean that is unknown and changes during training. Common dependence penalties and adversarial methods do not estimate this conditional mean; instead, they push predictions toward full independence. This stronger constraint can reduce accuracy even when average predictions are already equal. Existing conditional-mean methods are limited to linear predictors or low-dimensional sensitive attributes. We enable direct optimization of mean demographic parity using DPVar, a fairness measure defined as the variance of the conditional mean prediction. Because the conditional mean must be estimated as the predictor changes, optimizing DPVar leads to a functional bilevel problem. We develop two solvers: FBO, which uses a closed-form hypergradient, and an iterative-differentiation (ITD) solver that differentiates through updates of the conditional-mean estimator. Unlike previous conditional-mean methods, our approach applies to nonlinear predictors and high-dimensional continuous sensitive attributes. Across a semi-synthetic benchmark built from 21 tabular regression datasets and Communities & Crime data, FBO and ITD recover competitive or better accuracy-DPVar trade-offs than existing methods.
Related
- Fair Regression under Approximate Demographic Parity
- A deterministic analysis of a class of nonlinear regression methods
- Evaluation of a robust and asymmetric class of nonlinear regression models under censoring
- Bayes Factor Testing of Linear and Nonlinear Effects in Additive Gaussian Process Regression
- A Stochastic EM Algorithm with Sampling-Importance Resampling for Missing Data in Regression with Nonlinear Predictors
BibTeX
@misc{petrulionyte2026directly,
title = {{Directly Optimizing Mean Demographic Parity for Nonlinear Regression}},
author = {Ieva Petrulionyte and Julien Mairal and Michael Arbel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.05098},
eprint = {2607.05098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05098},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Directly Optimizing Mean Demographic Parity for Nonlinear Regression
AU - Ieva Petrulionyte
AU - Julien Mairal
AU - Michael Arbel
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2607.05098
UR - https://arxiv.org/abs/2607.05098
AB - We focus on regression settings where the fairness goal is to equalize average predictions across values of a sensitive attribute, a criterion known as mean demographic parity. Directly optimizing this criterion is difficult because it depends on a conditional mean that is unknown and changes during training. Common dependence penalties and adversarial methods do not estimate this conditional mean; instead, they push predictions toward full independence. This stronger constraint can reduce accuracy even when average predictions are already equal. Existing conditional-mean methods are limited to linear predictors or low-dimensional sensitive attributes. We enable direct optimization of mean demographic parity using DPVar, a fairness measure defined as the variance of the conditional mean prediction. Because the conditional mean must be estimated as the predictor changes, optimizing DPVar leads to a functional bilevel problem. We develop two solvers: FBO, which uses a closed-form hypergradient, and an iterative-differentiation (ITD) solver that differentiates through updates of the conditional-mean estimator. Unlike previous conditional-mean methods, our approach applies to nonlinear predictors and high-dimensional continuous sensitive attributes. Across a semi-synthetic benchmark built from 21 tabular regression datasets and Communities & Crime data, FBO and ITD recover competitive or better accuracy-DPVar trade-offs than existing methods.
ER -