# Bayes-Optimal Fair Classification with Linear Disparity Constraints via Pre-, In-, and Post-processing

arXiv: https://arxiv.org/abs/2402.02817 · HTML: https://mlsanity.com/paper/2402.02817/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2024.

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

- [A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems](https://mlsanity.com/paper/2407.12710/) (2024)
- [Machine Learning with Multitype Protected Attributes: Intersectional Fairness through Regularisation](https://mlsanity.com/paper/2509.08163/) (2025)
- [FairRR: Pre-Processing for Group Fairness through Randomized Response](https://mlsanity.com/paper/2403.07780/) (2024)
- [Audits Under Resource, Data, and Access Constraints: Scaling Laws For Less Discriminatory Alternatives](https://mlsanity.com/paper/2509.05627/) (2025)
- [Bayes-Optimal Fair Classification with Multiple Sensitive Features](https://mlsanity.com/paper/2505.00631/) (2025)
- [FedFACT: A Provable Framework for Controllable Group-Fairness Calibration in Federated Learning](https://mlsanity.com/paper/2506.03777/) (2025)
- [Group Fairness Meets the Black Box: Enabling Fair Algorithms on Closed LLMs via Post-Processing](https://mlsanity.com/paper/2508.11258/) (2025)
- [Fair Classification by Direct Intervention on Operating Characteristics](https://mlsanity.com/paper/2509.25481/) (2025)
- [Federated fairness-aware classification under differential privacy](https://mlsanity.com/paper/2603.24392/) (2026)
- [Demystifying the Optimal Fair Classifier in Multi-Class Classification](https://mlsanity.com/paper/2606.00656/) (2026)

## Abstract (arXiv)

Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We introduce the notion of linear disparity measures, which are linear functions of a probabilistic classifier; and bilinear disparity measures, which are also linear in the group-wise regression functions. We show that several popular disparity measures -- the deviations from demographic parity, equality of opportunity, and predictive equality -- are bilinear. We find the form of Bayes-optimal fair classifiers under a single linear disparity measure, by uncovering a connection with the Neyman-Pearson lemma. For bilinear disparity measures, we are able to find the explicit form of Bayes-optimal fair classifiers as group-wise thresholding rules with explicitly characterized thresholds. We develop similar algorithms for when protected attribute cannot be used at the prediction phase. Moreover, we obtain analogous theoretical characterizations of optimal classifiers for a multi-class protected attribute and for equalized odds. Leveraging our theoretical results, we design methods that learn fair Bayes-optimal classifiers under bilinear disparity constraints. Our methods cover three popular approaches to fairness-aware classification, via pre-processing (Fair Up- and Down-Sampling), in-processing (Fair cost-sensitive Classification) and post-processing (a Fair Plug-In Rule). Our methods control disparity directly while achieving near-optimal fairness-accuracy tradeoffs. We show empirically that our methods have state-of-the-art performance compared to existing algorithms. In particular, our pre-processing method can a reach higher accuracy than prior pre-processing methods at low disparity levels.