Fair Regression under Sample Selection Bias

TL;DR

This paper introduces a novel framework for fair regression that corrects sample selection bias using the Heckman model and Lagrange duality, ensuring fairness under various notions despite missing data.

Contribution

It extends fair regression to scenarios with sample selection bias by integrating the Heckman correction with fairness constraints, providing explicit formulas for key fairness notions.

Findings

Effective bias correction demonstrated on real datasets

Achieves fairness and utility without iterative optimization

Explicit formulas for mean difference and MSE difference

Abstract

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.