# Fair and Optimal Classification via Post-Processing

arXiv: https://arxiv.org/abs/2211.01528 · HTML: https://mlsanity.com/paper/2211.01528/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 89 references that are in the map.
- First posted on arXiv 3 Nov 2022.

## Builds on (most cited first, 30 of 40)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Gender Bias in Coreference Resolution: Evaluation and Debiasing Methods](https://mlsanity.com/paper/1804.06876/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [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)
- [Persistent Anti-Muslim Bias in Large Language Models](https://mlsanity.com/paper/2101.05783/) (2021)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [FA*IR: A Fair Top-k Ranking Algorithm](https://mlsanity.com/paper/1706.06368/) (2017)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Learning Controllable Fair Representations](https://mlsanity.com/paper/1812.04218/) (2018)
- [Scalable Fair Clustering](https://mlsanity.com/paper/1902.03519/) (2019)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [A Confidence-Based Approach for Balancing Fairness and Accuracy](https://mlsanity.com/paper/1601.05764/) (2016)

## Built on by (most cited first, 30 of 51)

- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [Representation Surgery: Theory and Practice of Affine Steering](https://mlsanity.com/paper/2402.09631/) (2024)
- [FFB: A Fair Fairness Benchmark for In-Processing Group Fairness Methods](https://mlsanity.com/paper/2306.09468/) (2023)
- [FRAPPE: A Group Fairness Framework for Post-Processing Everything](https://mlsanity.com/paper/2312.02592/) (2023)
- [Post-hoc Bias Scoring Is Optimal For Fair Classification](https://mlsanity.com/paper/2310.05725/) (2023)
- [LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch](https://mlsanity.com/paper/2409.02969/) (2024)
- [Counterfactual Fairness by Combining Factual and Counterfactual Predictions](https://mlsanity.com/paper/2409.01977/) (2024)
- [Differentially Private Post-Processing for Fair Regression](https://mlsanity.com/paper/2405.04034/) (2024)
- [A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems](https://mlsanity.com/paper/2407.12710/) (2024)
- [Post-Fair Federated Learning: Achieving Group and Community Fairness in Federated Learning via Post-processing](https://mlsanity.com/paper/2405.17782/) (2024)
- [Fairness-Aware Grouping for Continuous Sensitive Variables: Application for Debiasing Face Analysis with respect to Skin Tone](https://mlsanity.com/paper/2507.11247/) (2025)
- [Inducing Group Fairness in Prompt-Based Language Model Decisions](https://mlsanity.com/paper/2406.16738/) (2024)
- [Efficient Fairness-Performance Pareto Front Computation](https://mlsanity.com/paper/2409.17643/) (2024)
- [Fair Supervised Learning with A Simple Random Sampler of Sensitive Attributes](https://mlsanity.com/paper/2311.05866/) (2023)
- [Multi-Output Distributional Fairness via Post-Processing](https://mlsanity.com/paper/2409.00553/) (2024)
- [Demographic parity in regression and classification within the unawareness framework](https://mlsanity.com/paper/2409.02471/) (2024)
- [The Cost of Local and Global Fairness in Federated Learning](https://mlsanity.com/paper/2503.22762/) (2025)
- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [Meta Optimality for Demographic Parity Constrained Regression via Post-Processing](https://mlsanity.com/paper/2506.13947/) (2025)
- [FairAgent: Democratizing Fairness-Aware Machine Learning with LLM-Powered Agents](https://mlsanity.com/paper/2510.04317/) (2025)
- [Breaking the Dyadic Barrier: Rethinking Fairness in Link Prediction Beyond Demographic Parity](https://mlsanity.com/paper/2511.06568/) (2025)
- [Optimal Fair Aggregation of Crowdsourced Noisy Labels using Demographic Parity Constraints](https://mlsanity.com/paper/2601.23221/) (2026)
- [UMOEA/D: A Multiobjective Evolutionary Algorithm for Uniform Pareto Objectives based on Decomposition](https://mlsanity.com/paper/2402.09486/) (2024)
- [OTTER: Effortless Label Distribution Adaptation of Zero-shot Models](https://mlsanity.com/paper/2404.08461/) (2024)
- [AdapFair: Ensuring Adaptive Fairness for Machine Learning Operations](https://mlsanity.com/paper/2409.15088/) (2024)
- [Learning Pareto manifolds in high dimensions: How can regularization help?](https://mlsanity.com/paper/2503.08849/) (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)
- [FairNet: Dynamic Fairness Correction without Performance Loss via Contrastive Conditional LoRA](https://mlsanity.com/paper/2510.19421/) (2025)
- [Randomized multi-class classification under system constraints: a unified approach via post-processing](https://mlsanity.com/paper/2512.14246/) (2025)

## Abstract (arXiv)

To mitigate the bias exhibited by machine learning models, fairness criteria can be integrated into the training process to ensure fair treatment across all demographics, but it often comes at the expense of model performance. Understanding such tradeoffs, therefore, underlies the design of fair algorithms. To this end, this paper provides a complete characterization of the inherent tradeoff of demographic parity on classification problems, under the most general multi-group, multi-class, and noisy setting. Specifically, we show that the minimum error rate achievable by randomized and attribute-aware fair classifiers is given by the optimal value of a Wasserstein-barycenter problem. On the practical side, our findings lead to a simple post-processing algorithm that derives fair classifiers from score functions, which yields the optimal fair classifier when the score is Bayes optimal. We provide suboptimality analysis and sample complexity for our algorithm, and demonstrate its effectiveness on benchmark datasets.