# Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification

arXiv: https://arxiv.org/abs/1906.05082 · HTML: https://mlsanity.com/paper/1906.05082/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

## Built on by (most cited first, 30 of 60)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Data Collection and Quality Challenges in Deep Learning: A Data-Centric AI Perspective](https://mlsanity.com/paper/2112.06409/) (2021)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Sample Selection for Fair and Robust Training](https://mlsanity.com/paper/2110.14222/) (2021)
- [Your fairness may vary: Pretrained language model fairness in toxic text classification](https://mlsanity.com/paper/2108.01250/) (2021)
- [Fairness Reprogramming](https://mlsanity.com/paper/2209.10222/) (2022)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Bayes-Optimal Classifiers under Group Fairness](https://mlsanity.com/paper/2202.09724/) (2022)
- [Teacher's pet: understanding and mitigating biases in distillation](https://mlsanity.com/paper/2106.10494/) (2021)
- [Transferring Fairness under Distribution Shifts via Fair Consistency Regularization](https://mlsanity.com/paper/2206.12796/) (2022)
- [Aleatoric and Epistemic Discrimination: Fundamental Limits of Fairness Interventions](https://mlsanity.com/paper/2301.11781/) (2023)
- [Fair Bayes-Optimal Classifiers Under Predictive Parity](https://mlsanity.com/paper/2205.07182/) (2022)
- [Beyond Adult and COMPAS: Fairness in Multi-Class Prediction](https://mlsanity.com/paper/2206.07801/) (2022)
- [FRAPPE: A Group Fairness Framework for Post-Processing Everything](https://mlsanity.com/paper/2312.02592/) (2023)
- [Improving Fair Training under Correlation Shifts](https://mlsanity.com/paper/2302.02323/) (2023)
- [Fairness in Multi-Task Learning via Wasserstein Barycenters](https://mlsanity.com/paper/2306.10155/) (2023)
- [To the Fairness Frontier and Beyond: Identifying, Quantifying, and Optimizing the Fairness-Accuracy Pareto Frontier](https://mlsanity.com/paper/2206.00074/) (2022)
- [Fairness-aware Model-agnostic Positive and Unlabeled Learning](https://mlsanity.com/paper/2206.09346/) (2022)
- [FairGrad: Fairness Aware Gradient Descent](https://mlsanity.com/paper/2206.10923/) (2022)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Intrinsic Fairness-Accuracy Tradeoffs under Equalized Odds](https://mlsanity.com/paper/2405.07393/) (2024)
- [Estimating and Controlling for Equalized Odds via Sensitive Attribute Predictors](https://mlsanity.com/paper/2207.12497/) (2022)
- [FaiREE: Fair Classification with Finite-Sample and Distribution-Free Guarantee](https://mlsanity.com/paper/2211.15072/) (2022)
- [Adapting Fairness Interventions to Missing Values](https://mlsanity.com/paper/2305.19429/) (2023)
- [Arbitrariness Lies Beyond the Fairness-Accuracy Frontier](https://mlsanity.com/paper/2306.09425/) (2023)
- [How Far Can Fairness Constraints Help Recover From Biased Data?](https://mlsanity.com/paper/2312.10396/) (2023)
- [A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems](https://mlsanity.com/paper/2407.12710/) (2024)
- [Regression under demographic parity constraints via unlabeled post-processing](https://mlsanity.com/paper/2407.15453/) (2024)

## Abstract (arXiv)

We study the problem of fair binary classification using the notion of Equal Opportunity. It requires the true positive rate to distribute equally across the sensitive groups. Within this setting we show that the fair optimal classifier is obtained by recalibrating the Bayes classifier by a group-dependent threshold. We provide a constructive expression for the threshold. This result motivates us to devise a plug-in classification procedure based on both unlabeled and labeled datasets. While the latter is used to learn the output conditional probability, the former is used for calibration. The overall procedure can be computed in polynomial time and it is shown to be statistically consistent both in terms of the classification error and fairness measure. Finally, we present numerical experiments which indicate that our method is often superior or competitive with the state-of-the-art methods on benchmark datasets.