# Optimal Training of Fair Predictive Models

arXiv: https://arxiv.org/abs/1910.04109 · HTML: https://mlsanity.com/paper/1910.04109/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2019.

## Built on by (most cited first, 10 of 10)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Prompting Fairness: Integrating Causality to Debias Large Language Models](https://mlsanity.com/paper/2403.08743/) (2024)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Causal Fair Machine Learning via Rank-Preserving Interventional Distributions](https://mlsanity.com/paper/2307.12797/) (2023)
- [Group-blind optimal transport to group parity and its constrained variants](https://mlsanity.com/paper/2310.11407/) (2023)
- [Procedural Fairness Through Decoupling Objectionable Data Generating Components](https://mlsanity.com/paper/2311.14688/) (2023)
- [Fair Risk Minimization under Causal Path-Specific Effect Constraints](https://mlsanity.com/paper/2408.01630/) (2024)
- [Privilege Scores](https://mlsanity.com/paper/2502.01211/) (2025)
- [FairBelief -- Assessing Harmful Beliefs in Language Models](https://mlsanity.com/paper/2402.17389/) (2024)
- [Position: Beyond Sensitive Attributes, ML Fairness Should Quantify Structural Injustice via Social Determinants](https://mlsanity.com/paper/2508.08337/) (2025)

## Abstract (arXiv)

Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific causal constraints proposed by Nabi and Shpitser (2018), we introduce new theoretical results and optimization techniques to make model training easier and more accurate. Specifically, we show how to reparameterize the observed data likelihood such that fairness constraints correspond directly to parameters that appear in the likelihood, transforming a complex constrained optimization objective into a simple optimization problem with box constraints. We also exploit methods from empirical likelihood theory in statistics to improve predictive performance by constraining baseline covariates, without requiring parametric models. We combine the merits of both proposals to optimize a hybrid reparameterized likelihood. The techniques presented here should be applicable more broadly to fair prediction proposals that impose constraints on predictive models.