# Directly Optimizing Mean Demographic Parity for Nonlinear Regression

arXiv: https://arxiv.org/abs/2607.05098 · HTML: https://mlsanity.com/paper/2607.05098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 15 of 15)

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- [Do the rich get richer? An empirical analysis of the BitCoin transaction network](https://mlsanity.com/paper/1308.3892/) (2013)
- [NeutronStream: A Dynamic GNN Training Framework with Sliding Window for Graph Streams](https://mlsanity.com/paper/2312.02473/) (2023)
- [GNNFlow: A Distributed Framework for Continuous Temporal GNN Learning on Dynamic Graphs](https://mlsanity.com/paper/2311.17410/) (2023)
- [FastGL: A GPU-Efficient Framework for Accelerating Sampling-Based GNN Training at Large Scale](https://mlsanity.com/paper/2409.14939/) (2024)

## Abstract (arXiv)

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.