# Beyond Adult and COMPAS: Fairness in Multi-Class Prediction

arXiv: https://arxiv.org/abs/2206.07801 · HTML: https://mlsanity.com/paper/2206.07801/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 60 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 26 of 26)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [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)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [A comparative study of fairness-enhancing interventions in machine learning](https://mlsanity.com/paper/1802.04422/) (2018)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Learning Optimal and Fair Decision Trees for Non-Discriminative Decision-Making](https://mlsanity.com/paper/1903.10598/) (2019)
- [It's COMPASlicated: The Messy Relationship between RAI Datasets and Algorithmic Fairness Benchmarks](https://mlsanity.com/paper/2106.05498/) (2021)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)
- [Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values](https://mlsanity.com/paper/2109.10431/) (2021)
- [Group-Aware Threshold Adaptation for Fair Classification](https://mlsanity.com/paper/2111.04271/) (2021)
- [Envy-Free Classification](https://mlsanity.com/paper/1809.08700/) (2018)
- [Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms](https://mlsanity.com/paper/2012.12356/) (2020)
- [Fair for All: Best-effort Fairness Guarantees for Classification](https://mlsanity.com/paper/2012.10216/) (2020)
- [Optimized Score Transformation for Consistent Fair Classification](https://mlsanity.com/paper/1906.00066/) (2019)
- [A Note on the Convergence of ADMM for Linearly Constrained Convex Optimization Problems](https://mlsanity.com/paper/1507.02051/) (2015)

## Built on by (most cited first, 16 of 16)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [CLIP the Bias: How Useful is Balancing Data in Multimodal Learning?](https://mlsanity.com/paper/2403.04547/) (2024)
- [FRAPPE: A Group Fairness Framework for Post-Processing Everything](https://mlsanity.com/paper/2312.02592/) (2023)
- [Bottlenecks CLUB: Unifying Information-Theoretic Trade-offs Among Complexity, Leakage, and Utility](https://mlsanity.com/paper/2207.04895/) (2022)
- [KQ-SVD: Compressing the KV Cache with Provable Guarantees on Attention Fidelity](https://mlsanity.com/paper/2512.05916/) (2025)
- [Learning Optimal Fair Scoring Systems for Multi-Class Classification](https://mlsanity.com/paper/2304.05023/) (2023)
- [SQuat: Subspace-orthogonal KV Cache Quantization](https://mlsanity.com/paper/2503.24358/) (2025)
- [Toward responsible face datasets: modeling the distribution of a disentangled latent space for sampling face images from demographic groups](https://mlsanity.com/paper/2309.08442/) (2023)
- [Post-processing fairness with minimal changes](https://mlsanity.com/paper/2408.15096/) (2024)
- [On the Robustness of Text Vectorizers](https://mlsanity.com/paper/2303.07203/) (2023)
- [Bias Mitigation Methods for Binary Classification Decision-Making Systems: Survey and Recommendations](https://mlsanity.com/paper/2305.20020/) (2023)
- [Learning Pareto manifolds in high dimensions: How can regularization help?](https://mlsanity.com/paper/2503.08849/) (2025)
- [Understanding and Reducing the Class-Dependent Effects of Data Augmentation with A Two-Player Game Approach](https://mlsanity.com/paper/2407.03146/) (2024)
- [Controlled Model Debiasing through Minimal and Interpretable Updates](https://mlsanity.com/paper/2502.21284/) (2025)
- [Toward Unifying Group Fairness Evaluation from a Sparsity Perspective](https://mlsanity.com/paper/2511.00359/) (2025)
- [A Model Ensemble-Based Post-Processing Framework for Fairness-Aware Prediction](https://mlsanity.com/paper/2603.18838/) (2026)

## Abstract (arXiv)

We consider the problem of producing fair probabilistic classifiers for multi-class classification tasks. We formulate this problem in terms of "projecting" a pre-trained (and potentially unfair) classifier onto the set of models that satisfy target group-fairness requirements. The new, projected model is given by post-processing the outputs of the pre-trained classifier by a multiplicative factor. We provide a parallelizable iterative algorithm for computing the projected classifier and derive both sample complexity and convergence guarantees. Comprehensive numerical comparisons with state-of-the-art benchmarks demonstrate that our approach maintains competitive performance in terms of accuracy-fairness trade-off curves, while achieving favorable runtime on large datasets. We also evaluate our method at scale on an open dataset with multiple classes, multiple intersectional protected groups, and over 1M samples.