# Bayes-Optimal Fair Classification with Multiple Sensitive Features

arXiv: https://arxiv.org/abs/2505.00631 · HTML: https://mlsanity.com/paper/2505.00631/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 1 May 2025.

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

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [A Survey on Intersectional Fairness in Machine Learning: Notions, Mitigation, and Challenges](https://mlsanity.com/paper/2305.06969/) (2023)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [Post-hoc Bias Scoring Is Optimal For Fair Classification](https://mlsanity.com/paper/2310.05725/) (2023)
- [Bayes-Optimal Fair Classification with Linear Disparity Constraints via Pre-, In-, and Post-processing](https://mlsanity.com/paper/2402.02817/) (2024)
- [A Unified Post-Processing Framework for Group Fairness in Classification](https://mlsanity.com/paper/2405.04025/) (2024)

## Built on by (most cited first, 1 of 1)

- [Fairness May Backfire: When Leveling-Down Occurs in Fair Machine Learning](https://mlsanity.com/paper/2603.06901/) (2026)

## Abstract (arXiv)

Existing theoretical work on Bayes-optimal fair classifiers usually considers a single (binary) sensitive feature. In practice, individuals are often defined by multiple sensitive features. In this paper, we characterize the Bayes-optimal fair classifier for multiple sensitive features under general approximate fairness measures, including mean difference and mean ratio. We show that these approximate measures for existing group fairness notions, including Demographic Parity, Equal Opportunity, Predictive Equality, and Accuracy Parity, are linear transformations of selection rates for specific groups defined by both labels and sensitive features. We then characterize that Bayes-optimal fair classifiers for multiple sensitive features become instance-dependent thresholding rules that rely on a weighted sum of these group membership probabilities. Our framework applies to both attribute-aware and attribute-blind settings and can accommodate composite fairness notions like Equalized Odds. Building on this, we propose two practical algorithms for Bayes-optimal fair classification via in-processing and post-processing. We show empirically that our methods compare favorably to existing methods.