# Fairness Measures for Regression via Probabilistic Classification

arXiv: https://arxiv.org/abs/2001.06089 · HTML: https://mlsanity.com/paper/2001.06089/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2020.

## Built on by (most cited first, 11 of 11)

- [fairmodels: A Flexible Tool For Bias Detection, Visualization, And Mitigation](https://mlsanity.com/paper/2104.00507/) (2021)
- [TRIAGE: Characterizing and auditing training data for improved regression](https://mlsanity.com/paper/2310.18970/) (2023)
- [Flexible Group Fairness Metrics for Survival Analysis](https://mlsanity.com/paper/2206.03256/) (2022)
- [Practical Approaches for Fair Learning with Multitype and Multivariate Sensitive Attributes](https://mlsanity.com/paper/2211.06138/) (2022)
- [On the Consistency of Fairness Measurement Methods for Regression Tasks](https://mlsanity.com/paper/2406.13681/) (2024)
- [Machine Learning Fairness in House Price Prediction: A Case Study of America's Expanding Metropolises](https://mlsanity.com/paper/2505.01591/) (2025)
- [Fairness Perceptions in Regression-based Predictive Models](https://mlsanity.com/paper/2505.04886/) (2025)
- [Liouville PDE-based sliced-Wasserstein flow](https://mlsanity.com/paper/2505.17204/) (2025)
- [A Comprehensive Evaluation of the Sensitivity of Density-Ratio Estimation Based Fairness Measurement in Regression](https://mlsanity.com/paper/2508.14576/) (2025)
- [Wasserstein projection distance for fairness testing of regression models](https://mlsanity.com/paper/2510.04114/) (2025)
- [Comparative Separation: Evaluating Separation on Comparative Judgment Test Data](https://mlsanity.com/paper/2601.06761/) (2026)

## Abstract (arXiv)

Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems where the prediction is categorical, such as accepting or rejecting a loan application. This is in part because classification fairness measures are easily computed by comparing the rates of outcomes, leading to behaviours such as ensuring that the same fraction of eligible men are selected as eligible women. But such measures are computationally difficult to generalise to the continuous regression setting for problems such as pricing, or allocating payments. The difficulty arises from estimating conditional densities (such as the probability density that a system will over-charge by a certain amount). For the regression setting we introduce tractable approximations of the independence, separation and sufficiency criteria by observing that they factorise as ratios of different conditional probabilities of the protected attributes. We introduce and train machine learning classifiers, distinct from the predictor, as a mechanism to estimate these probabilities from the data. This naturally leads to model agnostic, tractable approximations of the criteria, which we explore experimentally.