# Fair Regression under Sample Selection Bias

arXiv: https://arxiv.org/abs/2110.04372 · HTML: https://mlsanity.com/paper/2110.04372/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 8 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [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)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Fairness-aware Agnostic Federated Learning](https://mlsanity.com/paper/2010.05057/) (2020)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Residual Unfairness in Fair Machine Learning from Prejudiced Data](https://mlsanity.com/paper/1806.02887/) (2018)
- [A Distributionally Robust Approach to Fair Classification](https://mlsanity.com/paper/2007.09530/) (2020)
- [Transfer of Machine Learning Fairness across Domains](https://mlsanity.com/paper/1906.09688/) (2019)
- [A General Framework for Fair Regression](https://mlsanity.com/paper/1810.05041/) (2018)
- [Fast Fair Regression via Efficient Approximations of Mutual Information](https://mlsanity.com/paper/2002.06200/) (2020)
- [Unfairness Discovery and Prevention For Few-Shot Regression](https://mlsanity.com/paper/2009.11406/) (2020)
- [Statistical Learning from Biased Training Samples](https://mlsanity.com/paper/1906.12304/) (2019)
- [Projection to Fairness in Statistical Learning](https://mlsanity.com/paper/2005.11720/) (2020)

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

- [A Robust Classifier Under Missing-Not-At-Random Sample Selection Bias](https://mlsanity.com/paper/2305.15641/) (2023)
- [On Prediction Feature Assignment in the Heckman Selection Model](https://mlsanity.com/paper/2309.08043/) (2023)
- [Sample Selection Bias in Machine Learning for Healthcare](https://mlsanity.com/paper/2405.07841/) (2024)

## Abstract (arXiv)

Recent research on fair regression focused on developing new fairness notions and approximation methods as target variables and even the sensitive attribute are continuous in the regression setting. However, all previous fair regression research assumed the training data and testing data are drawn from the same distributions. This assumption is often violated in real world due to the sample selection bias between the training and testing data. In this paper, we develop a framework for fair regression under sample selection bias when dependent variable values of a set of samples from the training data are missing as a result of another hidden process. Our framework adopts the classic Heckman model for bias correction and the Lagrange duality to achieve fairness in regression based on a variety of fairness notions. Heckman model describes the sample selection process and uses a derived variable called the Inverse Mills Ratio (IMR) to correct sample selection bias. We use fairness inequality and equality constraints to describe a variety of fairness notions and apply the Lagrange duality theory to transform the primal problem into the dual convex optimization. For the two popular fairness notions, mean difference and mean squared error difference, we derive explicit formulas without iterative optimization, and for Pearson correlation, we derive its conditions of achieving strong duality. We conduct experiments on three real-world datasets and the experimental results demonstrate the approach's effectiveness in terms of both utility and fairness metrics.