# Post-hoc Bias Scoring Is Optimal For Fair Classification

arXiv: https://arxiv.org/abs/2310.05725 · HTML: https://mlsanity.com/paper/2310.05725/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Fair Attribute Classification through Latent Space De-biasing](https://mlsanity.com/paper/2012.01469/) (2020)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Fair Contrastive Learning for Facial Attribute Classification](https://mlsanity.com/paper/2203.16209/) (2022)
- [Fair Classification with Group-Dependent Label Noise](https://mlsanity.com/paper/2011.00379/) (2020)
- [Robust Fairness under Covariate Shift](https://mlsanity.com/paper/2010.05166/) (2020)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Stability and Deviation Optimal Risk Bounds with Convergence Rate O(1/n)](https://mlsanity.com/paper/2103.12024/) (2021)
- [Regularization Matters: A Nonparametric Perspective on Overparametrized Neural Network](https://mlsanity.com/paper/2007.02486/) (2020)
- [Understanding Instance-Level Impact of Fairness Constraints](https://mlsanity.com/paper/2206.15437/) (2022)
- [Bayes-Optimal Classifiers under Group Fairness](https://mlsanity.com/paper/2202.09724/) (2022)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Group-Aware Threshold Adaptation for Fair Classification](https://mlsanity.com/paper/2111.04271/) (2021)
- [Weak Proxies are Sufficient and Preferable for Fairness with Missing Sensitive Attributes](https://mlsanity.com/paper/2210.03175/) (2022)

## Built on by (most cited first, 14 of 14)

- [Fairness Without Harm: An Influence-Guided Active Sampling Approach](https://mlsanity.com/paper/2402.12789/) (2024)
- [A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems](https://mlsanity.com/paper/2407.12710/) (2024)
- [FAIR-SIGHT: Fairness Assurance in Image Recognition via Simultaneous Conformal Thresholding and Dynamic Output Repair](https://mlsanity.com/paper/2504.07395/) (2025)
- [On the Maximal Local Disparity of Fairness-Aware Classifiers](https://mlsanity.com/paper/2406.03255/) (2024)
- [Meta Optimality for Demographic Parity Constrained Regression via Post-Processing](https://mlsanity.com/paper/2506.13947/) (2025)
- [LoGoFair: Post-Processing for Local and Global Fairness in Federated Learning](https://mlsanity.com/paper/2503.17231/) (2025)
- [Bayes-Optimal Fair Classification with Multiple Sensitive Features](https://mlsanity.com/paper/2505.00631/) (2025)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (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)
- [Metanetworks as Regulatory Operators: Learning to Edit for Requirement Compliance](https://mlsanity.com/paper/2512.15469/) (2025)
- [Fairness May Backfire: When Leveling-Down Occurs in Fair Machine Learning](https://mlsanity.com/paper/2603.06901/) (2026)
- [Demystifying the Optimal Fair Classifier in Multi-Class Classification](https://mlsanity.com/paper/2606.00656/) (2026)
- [Fairness Theatre: Evaluating Post-Hoc Fairness Interventions in Vendor-Controlled Early Warning Systems](https://mlsanity.com/paper/2609.38552/) (2026)

## Abstract (arXiv)

We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instance-level measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores.Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes.