Independence-based Fairness via CvM Regularization

Controlling fairness in machine learning model outputs is challenging due to complex, unstable and computationally expensive techniques for bias estimation on finite data samples. We propose a simple in-processing method to control group fairness during training by penalizing statistical dependence between model outputs $\hat{Y}$ and a sensitive attribute $S$. Our approach instantiates the Cramér--von Mises (CvM) dependence coefficient $\xi(S,\hat{Y})$ as a bounded, differentiable regularizer that integrates seamlessly with stochastic optimization. The resulting objective $L+\lambda \xi(S,\hat{Y})$ positions models along a fairness–utility Pareto frontier through a single multiplier $\lambda$. Our experiments demonstrate the effectiveness of this method for controlling the fairness-utility trade-off in both fairness-aware small and large tabular datasets. In order to control the compromise between fairness metrics and performance metrics, we propose a task-agnostic hyperparameter tuning pipeline and showcase its effectiveness in a large tabular dataset. In practice, we have observed that controlling for CvM leads to lower demographic-parity (DP) scores, providing a tractable and computationally efficient methodology, bridging the gap between policy requirements on DP and scalable training procedure for ML models.