Counterfactual Fairness by Combining Factual and Counterfactual Predictions
Zeyu Zhou, Tianci Liu, Ruqi Bai, Jing Gao, Murat Kocaoglu, David I. Inouye
TL;DR
This work analyzes Counterfactual Fairness (CF) within invertible causal models and shows that the Bayes-optimal predictor under CF can be constructed by mixing predictions at factual and counterfactual endpoints, yielding an optimal CF solution with predictable excess risk. It derives explicit excess-risk bounds for regression and classification tasks, tying them to the dependency between the target $Y$ and the sensitive attribute $A$ through the latent structure. To handle incomplete causal knowledge, the authors propose a Plug-in Counterfactual Fairness (PCF) approach and a Counterfactual Risk Minimization (CRM) strategy, providing guarantees when the counterfactual generator is estimated. Empirical results on synthetic and semi-synthetic data validate the theoretical insights, showing that PCF-based methods can outperform existing CF techniques in both perfect and imperfect counterfactual information regimes, with practical guidance on when and how to apply CRM. The work highlights the fundamental fairness-utility trade-off in CF and discusses limitations and future directions for deploying CF methods with real-world counterfactuals and pretrained predictors.
Abstract
In high-stake domains such as healthcare and hiring, the role of machine learning (ML) in decision-making raises significant fairness concerns. This work focuses on Counterfactual Fairness (CF), which posits that an ML model's outcome on any individual should remain unchanged if they had belonged to a different demographic group. Previous works have proposed methods that guarantee CF. Notwithstanding, their effects on the model's predictive performance remains largely unclear. To fill in this gap, we provide a theoretical study on the inherent trade-off between CF and predictive performance in a model-agnostic manner. We first propose a simple but effective method to cast an optimal but potentially unfair predictor into a fair one without losing the optimality. By analyzing its excess risk in order to achieve CF, we quantify this inherent trade-off. Further analysis on our method's performance with access to only incomplete causal knowledge is also conducted. Built upon it, we propose a performant algorithm that can be applied in such scenarios. Experiments on both synthetic and semi-synthetic datasets demonstrate the validity of our analysis and methods.