Auditing and Enforcing Conditional Fairness via Optimal Transport

Abstract: Conditional demographic parity (CDP) is a measure of the demographic parity of a predictive model or decision process when conditioning on an additional feature or set of features. Many algorithmic fairness techniques exist to target demographic parity, but CDP is much harder to achieve, particularly when the conditioning variable has many levels and/or when the model outputs are continuous. The problem of auditing and enforcing CDP is understudied in the literature. In light of this, we propose novel measures of {conditional demographic disparity (CDD)} which rely on statistical distances borrowed from the optimal transport literature. We further design and evaluate regularization-based approaches based on these CDD measures. Our methods, \fairbit{} and \fairlp{}, allow us to target CDP even when the conditioning variable has many levels. When model outputs are continuous, our methods target full equality of the conditional distributions, unlike other methods that only consider first moments or related proxy quantities. We validate the efficacy of our approaches on real-world datasets.

• The paper introduces optimal transport-based measures using the Wasserstein distance to capture conditional demographic disparities.
• It presents two regularization techniques, FairBiT and FairLeap, to enforce fairness while balancing model performance.
• Experiments on real-world datasets demonstrate that these methods achieve superior fairness-performance trade-offs compared to existing approaches.

Auditing and Enforcing Conditional Fairness via Optimal Transport

This paper introduces a novel approach to auditing and enforcing conditional demographic parity (CDP) using optimal transport techniques. CDP measures the fairness of a predictive model by ensuring its outputs remain independent of a sensitive feature when conditioned on an additional legitimate feature or set of features. Achieving CDP is more challenging than traditional demographic parity (DP) due to complexities introduced by multiple levels of conditioning variables and continuous model outputs.

Key Contributions:

1. Conditional Demographic Disparity (CDD) Measures: The authors propose new measures for CDD using statistical distances from the optimal transport literature, specifically the Wasserstein distance. These measures evaluate the entire conditional distribution rather than just first moments, applicable to both classification and regression settings.
2. Regularization Techniques:

To enforce CDP, the paper introduces two regularization-based approaches utilizing the CDD measures: - FairBiT (Fairness through Bi-causal Transport): This method uses the bi-causal transport distance to target equality of conditional distributions. The regularizer is derived from a nested form of the Wasserstein distance, providing a differentiable objective for optimization. - FairLeap: This method aggregates level-wise disparities across legitimate features using different probability measures. It allows practitioners to balance fairness and predictive performance through a regularization parameter.

1. Quantitative Evaluation: The paper conducts extensive experiments on real-world datasets, including classification and regression tasks, to demonstrate the efficacy of the proposed methods. FairBiT and FairLeap consistently achieve better fairness-performance trade-offs compared to existing methods such as DCFR and adversarial debiasing.

Implications:

The findings address a significant gap in algorithmic fairness by providing tools to measure and enforce CDP. These methods are particularly relevant in scenarios where legitimate features are numerous or continuous, situations where traditional methods struggle. By leveraging optimal transport, the paper introduces a mathematically grounded framework to evaluate and reduce unfairness in algorithmic decision-making.

Future Directions:

This research opens avenues for further exploration in conditional fairness:

• Extending bi-causal transport methods to other fairness notions like equalized odds.
• Exploring hybrid approaches combining FairBiT with pre-processing or adversarial techniques to enhance fairness-performance trade-offs.
• Investigating applications to fairness-aware synthetic data generation for sectors like healthcare.

Overall, this paper contributes a substantial methodological advancement for achieving fairness in machine learning models by redefining fairness measures through the lens of optimal transport.