{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.05098",
  "author_total": 3,
  "authors": [
    {
      "name": "Ieva Petrulionyte"
    },
    {
      "name": "Julien Mairal"
    },
    {
      "name": "Michael Arbel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6d7twqgaxfc5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05098",
  "fulltext_url": null,
  "id": "6d7twqgaxfc5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.05098",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "3311|Ethics and Social Impacts of AI"
    ]
  ],
  "openalex": "W7167624761",
  "pdf_url": "https://arxiv.org/pdf/2607.05098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6d7twqgaxfc5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:03Z",
      "native_id": "2607.05098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Directly Optimizing Mean Demographic Parity for Nonlinear Regression",
  "title_text": "Directly Optimizing Mean Demographic Parity for Nonlinear Regression",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/6d7twqgaxfc5g",
  "venue": "arXiv",
  "versions": []
}