# Extending Fair Null-Space Projections for Continuous Attributes to Kernel Methods

arXiv: https://arxiv.org/abs/2511.03304 · HTML: https://mlsanity.com/paper/2511.03304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [It's COMPASlicated: The Messy Relationship between RAI Datasets and Algorithmic Fairness Benchmarks](https://mlsanity.com/paper/2106.05498/) (2021)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Kernelized Concept Erasure](https://mlsanity.com/paper/2201.12191/) (2022)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [General Fair Empirical Risk Minimization](https://mlsanity.com/paper/1901.10080/) (2019)
- [Learning Fair Representations for Kernel Models](https://mlsanity.com/paper/1906.11813/) (2019)
- [Spectral Algorithms for Computing Fair Support Vector Machines](https://mlsanity.com/paper/1710.05895/) (2017)
- [Generalized Disparate Impact for Configurable Fairness Solutions in ML](https://mlsanity.com/paper/2305.18504/) (2023)
- [Fair Representation Learning for Continuous Sensitive Attributes using Expectation of Integral Probability Metrics](https://mlsanity.com/paper/2505.06435/) (2025)
- [Oblivious Data for Fairness with Kernels](https://mlsanity.com/paper/2002.02901/) (2020)
- [FairICP: Encouraging Equalized Odds via Inverse Conditional Permutation](https://mlsanity.com/paper/2404.05678/) (2024)

## Abstract (arXiv)

With the on-going integration of machine learning systems into the everyday social life of millions the notion of fairness becomes an ever increasing priority in their development. Fairness notions commonly rely on protected attributes to assess potential biases. Here, the majority of literature focuses on discrete setups regarding both target and protected attributes. The literature on continuous attributes especially in conjunction with regression -- we refer to this as continuous fairness -- is scarce. A common strategy is iterative null-space projection which as of now has only been explored for linear models or embeddings such as obtained by a non-linear encoder. We improve on this by extending this to kernel induced feature spaces by means of the ``empirical feature space''. We theoretically derive this as a direct transformation of the kernel matrix yielding a model and fairness-score agnostic method applicable to continuous protected attributes. We demonstrate that our novel approach in conjunction with Support Vector Regression (SVR) provides competitive or improved performance across multiple datasets in comparison to other contemporary methods.