# Understanding and Mitigating Accuracy Disparity in Regression

arXiv: https://arxiv.org/abs/2102.12013 · HTML: https://mlsanity.com/paper/2102.12013/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 58 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [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)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations](https://mlsanity.com/paper/1707.00075/) (2017)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Why Is My Classifier Discriminatory?](https://mlsanity.com/paper/1805.12002/) (2018)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization](https://mlsanity.com/paper/1807.03907/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Classification vs regression in overparameterized regimes: Does the loss function matter?](https://mlsanity.com/paper/2005.08054/) (2020)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Removing Spurious Features can Hurt Accuracy and Affect Groups Disproportionately](https://mlsanity.com/paper/2012.04104/) (2020)
- [Fairness Through Causal Awareness: Learning Latent-Variable Models for Biased Data](https://mlsanity.com/paper/1809.02519/) (2018)
- [Fundamental Limits and Tradeoffs in Invariant Representation Learning](https://mlsanity.com/paper/2012.10713/) (2020)
- [Fair Regression for Health Care Spending](https://mlsanity.com/paper/1901.10566/) (2019)
- [An implicit function learning approach for parametric modal regression](https://mlsanity.com/paper/2002.06195/) (2020)
- [Feature Noise Induces Loss Discrepancy Across Groups](https://mlsanity.com/paper/1911.09876/) (2019)

## Built on by (most cited first, 17 of 17)

- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [Subgroup Robustness Grows On Trees: An Empirical Baseline Investigation](https://mlsanity.com/paper/2211.12703/) (2022)
- [Equal Opportunity of Coverage in Fair Regression](https://mlsanity.com/paper/2311.02243/) (2023)
- [Towards Return Parity in Markov Decision Processes](https://mlsanity.com/paper/2111.10476/) (2021)
- [Understanding the Impact of Adversarial Robustness on Accuracy Disparity](https://mlsanity.com/paper/2211.15762/) (2022)
- [Costs and Benefits of Fair Regression](https://mlsanity.com/paper/2106.08812/) (2021)
- [Mean Parity Fair Regression in RKHS](https://mlsanity.com/paper/2302.10409/) (2023)
- [Adapting Static Fairness to Sequential Decision-Making: Bias Mitigation Strategies towards Equal Long-term Benefit Rate](https://mlsanity.com/paper/2309.03426/) (2023)
- [Differentially Private Post-Processing for Fair Regression](https://mlsanity.com/paper/2405.04034/) (2024)
- [Fairness-aware Regression Robust to Adversarial Attacks](https://mlsanity.com/paper/2211.04449/) (2022)
- [Challenges and Opportunities in Improving Worst-Group Generalization in Presence of Spurious Features](https://mlsanity.com/paper/2306.11957/) (2023)
- [Pursuing Overall Welfare in Federated Learning through Sequential Decision Making](https://mlsanity.com/paper/2405.20821/) (2024)
- [Intersectional Divergence: Measuring Fairness in Regression](https://mlsanity.com/paper/2505.00830/) (2025)
- [RPWithPrior: Label Differential Privacy in Regression](https://mlsanity.com/paper/2601.22625/) (2026)
- [Alpha and Prejudice: Improving α-sized Worst-case Fairness via Intrinsic Reweighting](https://mlsanity.com/paper/2411.03068/) (2024)
- [Wasserstein projection distance for fairness testing of regression models](https://mlsanity.com/paper/2510.04114/) (2025)
- [StackingNet: Collective Inference Across Independent AI Foundation Models](https://mlsanity.com/paper/2602.13792/) (2026)

## Abstract (arXiv)

With the widespread deployment of large-scale prediction systems in high-stakes domains, e.g., face recognition, criminal justice, etc., disparity in prediction accuracy between different demographic subgroups has called for fundamental understanding on the source of such disparity and algorithmic intervention to mitigate it. In this paper, we study the accuracy disparity problem in regression. To begin with, we first propose an error decomposition theorem, which decomposes the accuracy disparity into the distance between marginal label distributions and the distance between conditional representations, to help explain why such accuracy disparity appears in practice. Motivated by this error decomposition and the general idea of distribution alignment with statistical distances, we then propose an algorithm to reduce this disparity, and analyze its game-theoretic optima of the proposed objective functions. To corroborate our theoretical findings, we also conduct experiments on five benchmark datasets. The experimental results suggest that our proposed algorithms can effectively mitigate accuracy disparity while maintaining the predictive power of the regression models.