Methods to tune fairness in regression predictions across groups
Fair Regression under Approximate Demographic Parity
Machine Learning
Summary
Sometimes predictions made by computers about people's outcomes can be unfair to certain groups. This paper looks at ways to make predictions more fair by allowing some differences but keeping those differences limited using a mathematical measure called Wasserstein distance. The authors show that this approach can balance fairness and accuracy better than demanding exact equality. They provide formulas and methods that can be used in real-world data, like survey data from California, to adjust predictions while maintaining fairness.
What this means in practice
- •For data scientists: Create regression models with controllable fairness levels between demographic groups using Wasserstein distance constraints.
- •For social policy analytics teams: Adjust predictions in social data to balance accuracy and fairness, demonstrated on California demographic survey data.
Authors
Weiwei Wang, Xianyang Zhang, Raymond K. W. Wong
Abstract
Exact demographic parity requires the same prediction distribution across sensitive groups. In regression, this can be too restrictive and reduce predictive accuracy. We instead bound every pairwise Wasserstein distance between group-specific prediction distributions by a chosen tolerance, allowing the groups to differ while keeping fairness tunable. On the real line, the prediction and constrained transport problems have the same infimum. If the transport problem attains this value and suitable Monge maps exist, a deterministic transport-form predictor realizes it. Under a standard one-dimensional condition, the problem becomes a bounded quantile optimization that is convex when the conditional expected loss is convex in prediction. Under squared loss with two positively weighted groups, the $W_1$, $W_2$, and $W_\infty$ constraints yield soft-thresholding, shrinkage, and clipping. Under the stated conditions, we establish rates for the known-cost plug-in estimator. When the cost is unavailable, we describe an observed-loss computational proxy. Synthetic and California 2018 ACS studies illustrate the tunable fairness-accuracy trade-off and distinguish calibration feasibility from held-out fairness and accuracy.