# Fair Bayes-Optimal Classifiers Under Predictive Parity

arXiv: https://arxiv.org/abs/2205.07182 · HTML: https://mlsanity.com/paper/2205.07182/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 61 references that are in the map.
- First posted on arXiv 15 May 2022.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [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)
- [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)
- [Men Also Like Shopping: Reducing Gender Bias Amplification using Corpus-level Constraints](https://mlsanity.com/paper/1707.09457/) (2017)
- [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)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Towards Fairness in Visual Recognition: Effective Strategies for Bias Mitigation](https://mlsanity.com/paper/1911.11834/) (2019)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [FairGAN: Fairness-aware Generative Adversarial Networks](https://mlsanity.com/paper/1805.11202/) (2018)
- [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)
- [Achieving Fairness through Adversarial Learning: an Application to Recidivism Prediction](https://mlsanity.com/paper/1807.00199/) (2018)
- [A Confidence-Based Approach for Balancing Fairness and Accuracy](https://mlsanity.com/paper/1601.05764/) (2016)
- [Learning Certified Individually Fair Representations](https://mlsanity.com/paper/2002.10312/) (2020)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [iFair: Learning Individually Fair Data Representations for Algorithmic Decision Making](https://mlsanity.com/paper/1806.01059/) (2018)

## 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)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Can LLMs Recognize Toxicity? A Structured Investigation Framework and Toxicity Metric](https://mlsanity.com/paper/2402.06900/) (2024)
- [Aleatoric and Epistemic Discrimination: Fundamental Limits of Fairness Interventions](https://mlsanity.com/paper/2301.11781/) (2023)
- [SYNAuG: Exploiting Synthetic Data for Data Imbalance Problems](https://mlsanity.com/paper/2308.00994/) (2023)
- [How Far Can Fairness Constraints Help Recover From Biased Data?](https://mlsanity.com/paper/2312.10396/) (2023)
- [Achieving Group Fairness through Independence in Predictive Process Monitoring](https://mlsanity.com/paper/2412.04914/) (2024)
- [Group-blind optimal transport to group parity and its constrained variants](https://mlsanity.com/paper/2310.11407/) (2023)
- [FairRR: Pre-Processing for Group Fairness through Randomized Response](https://mlsanity.com/paper/2403.07780/) (2024)
- [Demographic parity in regression and classification within the unawareness framework](https://mlsanity.com/paper/2409.02471/) (2024)
- [On Optimal Steering to Achieve Exact Fairness](https://mlsanity.com/paper/2509.15759/) (2025)
- [An Operational Perspective to Fairness Interventions: Where and How to Intervene](https://mlsanity.com/paper/2302.01574/) (2023)
- [Randomized multi-class classification under system constraints: a unified approach via post-processing](https://mlsanity.com/paper/2512.14246/) (2025)
- [EquiPy: Sequential Fairness using Optimal Transport in Python](https://mlsanity.com/paper/2503.09866/) (2025)
- [Fair Decisions from Calibrated Scores: Achieving Optimal Classification While Satisfying Sufficiency](https://mlsanity.com/paper/2602.07285/) (2026)
- [A Comprehensive View of Fairness through Distributional Stability](https://mlsanity.com/paper/2609.37061/) (2026)

## Abstract (arXiv)

Increasing concerns about disparate effects of AI have motivated a great deal of work on fair machine learning. Existing works mainly focus on independence- and separation-based measures (e.g., demographic parity, equality of opportunity, equalized odds), while sufficiency-based measures such as predictive parity are much less studied. This paper considers predictive parity, which requires equalizing the probability of success given a positive prediction among different protected groups. We prove that, if the overall performances of different groups vary only moderately, all fair Bayes-optimal classifiers under predictive parity are group-wise thresholding rules. Perhaps surprisingly, this may not hold if group performance levels vary widely; in this case we find that predictive parity among protected groups may lead to within-group unfairness. We then propose an algorithm we call FairBayes-DPP, aiming to ensure predictive parity when our condition is satisfied. FairBayes-DPP is an adaptive thresholding algorithm that aims to achieve predictive parity, while also seeking to maximize test accuracy. We provide supporting experiments conducted on synthetic and empirical data.