# Selective Regression Under Fairness Criteria

arXiv: https://arxiv.org/abs/2110.15403 · HTML: https://mlsanity.com/paper/2110.15403/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 72 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 30 of 35)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [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)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (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)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [A Clarification of the Nuances in the Fairness Metrics Landscape](https://mlsanity.com/paper/2106.00467/) (2021)
- [Classification vs regression in overparameterized regimes: Does the loss function matter?](https://mlsanity.com/paper/2005.08054/) (2020)
- [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Learning Optimal Fair Policies](https://mlsanity.com/paper/1809.02244/) (2018)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [Selective Classification Can Magnify Disparities Across Groups](https://mlsanity.com/paper/2010.14134/) (2020)
- [Regression with reject option and application to kNN](https://mlsanity.com/paper/2006.16597/) (2020)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [General Fair Empirical Risk Minimization](https://mlsanity.com/paper/1901.10080/) (2019)

## Built on by (most cited first, 30 of 34)

- [Calibrated Selective Classification](https://mlsanity.com/paper/2208.12084/) (2022)
- [Regression with Multi-Expert Deferral](https://mlsanity.com/paper/2403.19494/) (2024)
- [Realizable H-Consistent and Bayes-Consistent Loss Functions for Learning to Defer](https://mlsanity.com/paper/2407.13732/) (2024)
- [Effective Human-AI Teams via Learned Natural Language Rules and Onboarding](https://mlsanity.com/paper/2311.01007/) (2023)
- [Fairness through Aleatoric Uncertainty](https://mlsanity.com/paper/2304.03646/) (2023)
- [Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer](https://mlsanity.com/paper/2506.20650/) (2025)
- [Coarse race data conceals disparities in clinical risk score performance](https://mlsanity.com/paper/2304.09270/) (2023)
- [Budgeted Multiple-Expert Deferral](https://mlsanity.com/paper/2510.26706/) (2025)
- [Regression with Cost-based Rejection](https://mlsanity.com/paper/2311.04550/) (2023)
- [Fair Classifiers that Abstain without Harm](https://mlsanity.com/paper/2310.06205/) (2023)
- [HealthMamba: An Uncertainty-aware Spatiotemporal Graph State Space Model for Effective and Reliable Healthcare Facility Visit Prediction](https://mlsanity.com/paper/2602.05286/) (2026)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [How Far Can Fairness Constraints Help Recover From Biased Data?](https://mlsanity.com/paper/2312.10396/) (2023)
- [Conformalized Selective Regression](https://mlsanity.com/paper/2402.16300/) (2024)
- [Fairness-aware Regression Robust to Adversarial Attacks](https://mlsanity.com/paper/2211.04449/) (2022)
- [Learning to Partially Defer for Sequences](https://mlsanity.com/paper/2502.01459/) (2025)
- [Improving Predictor Reliability with Selective Recalibration](https://mlsanity.com/paper/2410.05407/) (2024)
- [Fairness Overfitting in Machine Learning: An Information-Theoretic Perspective](https://mlsanity.com/paper/2506.07861/) (2025)
- [Group Fairness with Uncertainty in Sensitive Attributes](https://mlsanity.com/paper/2302.08077/) (2023)
- [When No-Rejection Learning is Consistent for Regression with Rejection](https://mlsanity.com/paper/2307.02932/) (2023)
- [Selective Explanations](https://mlsanity.com/paper/2405.19562/) (2024)
- [The Approximate Fisher Influence Function: Faster Estimation of Data Influence in Statistical Models](https://mlsanity.com/paper/2407.08169/) (2024)
- [FairlyUncertain: A Comprehensive Benchmark of Uncertainty in Algorithmic Fairness](https://mlsanity.com/paper/2410.02005/) (2024)
- [Interpretable and Fair Mechanisms for Abstaining Classifiers](https://mlsanity.com/paper/2503.18826/) (2025)
- [Selective Prediction Reduces the Negative Effects of Automation Bias Overall but Increases False Negatives](https://mlsanity.com/paper/2508.07617/) (2025)
- [Optimized Deferral for Imbalanced Settings](https://mlsanity.com/paper/2604.27723/) (2026)
- [Reweighting Improves Conditional Risk Bounds](https://mlsanity.com/paper/2501.02353/) (2025)
- [RPWithPrior: Label Differential Privacy in Regression](https://mlsanity.com/paper/2601.22625/) (2026)
- [Calibrating conditional risk](https://mlsanity.com/paper/2604.20409/) (2026)
- [Selective Time Series Forecasting via Metalearning](https://mlsanity.com/paper/2606.23448/) (2026)

## Abstract (arXiv)

Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of reducing coverage (i.e., by predicting on fewer samples). However, as we show, in some cases, the performance of a minority subgroup can decrease while we reduce the coverage, and thus selective regression can magnify disparities between different sensitive subgroups. Motivated by these disparities, we propose new fairness criteria for selective regression requiring the performance of every subgroup to improve with a decrease in coverage. We prove that if a feature representation satisfies the sufficiency criterion or is calibrated for mean and variance, than the proposed fairness criteria is met. Further, we introduce two approaches to mitigate the performance disparity across subgroups: (a) by regularizing an upper bound of conditional mutual information under a Gaussian assumption and (b) by regularizing a contrastive loss for conditional mean and conditional variance prediction. The effectiveness of these approaches is demonstrated on synthetic and real-world datasets.