# Machine Learning with Multitype Protected Attributes: Intersectional Fairness through Regularisation

arXiv: https://arxiv.org/abs/2509.08163 · HTML: https://mlsanity.com/paper/2509.08163/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 109 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Builds on (most cited first, 30 of 39)

- [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)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)
- [Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations](https://mlsanity.com/paper/1707.00075/) (2017)
- [Model Evaluation, Model Selection, and Algorithm Selection in Machine Learning](https://mlsanity.com/paper/1811.12808/) (2018)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [To be Robust or to be Fair: Towards Fairness in Adversarial Training](https://mlsanity.com/paper/2010.06121/) (2020)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Achieving Fairness through Adversarial Learning: an Application to Recidivism Prediction](https://mlsanity.com/paper/1807.00199/) (2018)
- [Putting Fairness Principles into Practice: Challenges, Metrics, and Improvements](https://mlsanity.com/paper/1901.04562/) (2019)
- [Post-processing for Individual Fairness](https://mlsanity.com/paper/2110.13796/) (2021)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)
- [Algorithmic Fairness Datasets: the Story so Far](https://mlsanity.com/paper/2202.01711/) (2022)
- [Towards Fair Classifiers Without Sensitive Attributes: Exploring Biases in Related Features](https://mlsanity.com/paper/2104.14537/) (2021)
- [Characterizing Intersectional Group Fairness with Worst-Case Comparisons](https://mlsanity.com/paper/2101.01673/) (2021)
- [A Survey on Intersectional Fairness in Machine Learning: Notions, Mitigation, and Challenges](https://mlsanity.com/paper/2305.06969/) (2023)
- [A survey of bias in Machine Learning through the prism of Statistical Parity for the Adult Data Set](https://mlsanity.com/paper/2003.14263/) (2020)
- [A Stochastic Optimization Framework for Fair Risk Minimization](https://mlsanity.com/paper/2102.12586/) (2021)
- [Improved Adversarial Learning for Fair Classification](https://mlsanity.com/paper/1901.10443/) (2019)
- [Fairness in Clustering with Multiple Sensitive Attributes](https://mlsanity.com/paper/1910.05113/) (2019)
- [Partial Distance Correlation with Methods for Dissimilarities](https://mlsanity.com/paper/1310.2926/) (2013)
- [InfoFair: Information-Theoretic Intersectional Fairness](https://mlsanity.com/paper/2105.11069/) (2021)
- [Fast Computing for Distance Covariance](https://mlsanity.com/paper/1410.1503/) (2014)

## Built on by (most cited first, 3 of 3)

- [Data-Driven Analysis of Intersectional Bias in Image Classification: A Framework with Bias-Weighted Augmentation](https://mlsanity.com/paper/2510.16072/) (2025)
- [Fairness-Aware Insurance Pricing: A Multi-Objective Optimization Approach](https://mlsanity.com/paper/2512.24747/) (2025)
- [Multi-Sensitive Distributional Fairness: Joint Wasserstein Audits and Shapley Allocation](https://mlsanity.com/paper/2610.19252/) (2026)

## Abstract (arXiv)

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.