# Mean Parity Fair Regression in RKHS

arXiv: https://arxiv.org/abs/2302.10409 · HTML: https://mlsanity.com/paper/2302.10409/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 55 references that are in the map.
- First posted on arXiv 21 Feb 2023.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [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)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [Stable and Fair Classification](https://mlsanity.com/paper/1902.07823/) (2019)
- [General Fair Empirical Risk Minimization](https://mlsanity.com/paper/1901.10080/) (2019)
- [Fast Randomized Kernel Methods With Statistical Guarantees](https://mlsanity.com/paper/1411.0306/) (2014)
- [Fair Forests: Regularized Tree Induction to Minimize Model Bias](https://mlsanity.com/paper/1712.08197/) (2017)
- [Learning Fair Representations for Kernel Models](https://mlsanity.com/paper/1906.11813/) (2019)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)
- [Achieving Fairness with a Simple Ridge Penalty](https://mlsanity.com/paper/2105.13817/) (2021)
- [Fast Fair Regression via Efficient Approximations of Mutual Information](https://mlsanity.com/paper/2002.06200/) (2020)
- [On the Complexity of Learning with Kernels](https://mlsanity.com/paper/1411.1158/) (2014)
- [Two-stage Algorithm for Fairness-aware Machine Learning](https://mlsanity.com/paper/1710.04924/) (2017)
- [Oblivious Data for Fairness with Kernels](https://mlsanity.com/paper/2002.02901/) (2020)
- [Learning Fair Canonical Polyadical Decompositions using a Kernel Independence Criterion](https://mlsanity.com/paper/2104.13504/) (2021)
- [Fair Kernel Regression via Fair Feature Embedding in Kernel Space](https://mlsanity.com/paper/1907.02242/) (2019)

## Built on by (most cited first, 6 of 6)

- [Neural Polarizer: A Lightweight and Effective Backdoor Defense via Purifying Poisoned Features](https://mlsanity.com/paper/2306.16697/) (2023)
- [Standardized Interpretable Fairness Measures for Continuous Risk Scores](https://mlsanity.com/paper/2308.11375/) (2023)
- [Class-Conditional Neural Polarizer: A Lightweight and Effective Backdoor Defense by Purifying Poisoned Features](https://mlsanity.com/paper/2502.18520/) (2025)
- [FairMT: Fairness for Heterogeneous Multi-Task Learning](https://mlsanity.com/paper/2512.00469/) (2025)
- [The Pok'emon Theorem and other Fairness Impossibility Results](https://mlsanity.com/paper/2605.09221/) (2026)
- [Differentiable Optimization Layers for Guaranteed Fairness in Deep Learning](https://mlsanity.com/paper/2605.17118/) (2026)

## Abstract (arXiv)

We study the fair regression problem under the notion of Mean Parity (MP) fairness, which requires the conditional mean of the learned function output to be constant with respect to the sensitive attributes. We address this problem by leveraging reproducing kernel Hilbert space (RKHS) to construct the functional space whose members are guaranteed to satisfy the fairness constraints. The proposed functional space suggests a closed-form solution for the fair regression problem that is naturally compatible with multiple sensitive attributes. Furthermore, by formulating the fairness-accuracy tradeoff as a relaxed fair regression problem, we derive a corresponding regression function that can be implemented efficiently and provides interpretable tradeoffs. More importantly, under some mild assumptions, the proposed method can be applied to regression problems with a covariance-based notion of fairness. Experimental results on benchmark datasets show the proposed methods achieve competitive and even superior performance compared with several state-of-the-art methods.