[Paper Review] A Sequentially Fair Mechanism for Multiple Sensitive Attributes

François Hu, Philipp Ratz+1 more|arXiv (Cornell University)|Sep 12, 2023

Health Systems, Economic Evaluations, Quality of Life4 citations

TL;DR

This paper proposes a sequentially fair mechanism for multiple sensitive attributes (MSA) using multi-marginal Wasserstein barycenters to achieve exact and approximate fairness in post-processing predictions. The method ensures order-invariant fair outcomes across sensitive features while enabling targeted fairness prioritization and offering a closed-form solution with strong empirical performance on synthetic and real-world datasets.

ABSTRACT

In the standard use case of Algorithmic Fairness, the goal is to eliminate the relationship between a sensitive variable and a corresponding score. Throughout recent years, the scientific community has developed a host of definitions and tools to solve this task, which work well in many practical applications. However, the applicability and effectivity of these tools and definitions becomes less straightfoward in the case of multiple sensitive attributes. To tackle this issue, we propose a sequential framework, which allows to progressively achieve fairness across a set of sensitive features. We accomplish this by leveraging multi-marginal Wasserstein barycenters, which extends the standard notion of Strong Demographic Parity to the case with multiple sensitive characteristics. This method also provides a closed-form solution for the optimal, sequentially fair predictor, permitting a clear interpretation of inter-sensitive feature correlations. Our approach seamlessly extends to approximate fairness, enveloping a framework accommodating the trade-off between risk and unfairness. This extension permits a targeted prioritization of fairness improvements for a specific attribute within a set of sensitive attributes, allowing for a case specific adaptation. A data-driven estimation procedure for the derived solution is developed, and comprehensive numerical experiments are conducted on both synthetic and real datasets. Our empirical findings decisively underscore the practical efficacy of our post-processing approach in fostering fair decision-making.

Motivation & Objective

• To address the limitations of single-sensitive-attribute fairness methods in handling intersectional bias from multiple sensitive attributes.
• To develop a post-processing framework that ensures fairness across multiple sensitive features without compromising predictive performance.
• To enable flexible, prioritized fairness improvements by allowing approximate fairness constraints for specific attributes.
• To provide a closed-form, interpretable solution that quantifies inter-sensitive feature correlations in fairness corrections.
• To empirically validate the method’s effectiveness in reducing unfairness while maintaining high predictive accuracy across diverse datasets.

Proposed method

• The method constructs multi-marginal 2-Wasserstein barycenters to generalize Strong Demographic Parity to multiple sensitive attributes.
• It reformulates the optimal fair predictor in a sequential form using the associativity of Wasserstein barycenters, ensuring consistent outcomes regardless of correction order.
• The approach supports approximate fairness by introducing adjustable fairness constraints, allowing trade-offs between risk and unfairness.
• A data-driven estimation procedure is developed to compute the barycenter from empirical distributions, enabling practical deployment.
• The framework allows prioritization of fairness improvements for specific attributes by tuning individual fairness constraint parameters.
• The method is applied post-hoc to any off-the-shelf predictor, preserving its original performance while correcting for bias.

Figure 1: Synthetic data with $\boldsymbol{\tau}=(0,0.05,0.1)$ . A sequential unfairness evaluation, $\mathcal{U}_{3}$ , of ( left pane ) exact fairness, ( middle ) approximate $A_{1:3}$ -fairness with $\boldsymbol{\varepsilon}$ -RI where $\boldsymbol{\varepsilon}=\varepsilon_{1,2,3}=(0.2,0.5,0.75)$

Experimental results

Research questions

• RQ1 How can fairness be consistently achieved across multiple sensitive attributes without dependency on the order of correction?
• RQ2 What is the optimal way to generalize Demographic Parity to multiple sensitive attributes using optimal transport?
• RQ3 How can fairness constraints be flexibly prioritized for specific attributes in a multi-attribute setting?
• RQ4 What is the impact of approximate fairness on predictive performance and subgroup fairness?
• RQ5 How do inter-sensitive feature correlations influence the fairness correction process and outcomes?

Key findings

• The proposed method achieves exact fairness with order-invariant predictions, regardless of the sequence in which sensitive attributes are corrected.
• On the Adult dataset, the method reduced unfairness from 0.18 to 0.03 while maintaining F1 of 0.90, outperforming Fairlearn (0.08 unfairness) and FairBalance (0.16 unfairness).
• In the tunadromd dataset with 10 sensitive attributes, the method reduced unfairness from 3.77 to 1.05, demonstrating scalability to high-dimensional sensitive spaces.
• The method enables targeted fairness improvements: adjusting ε for one attribute (e.g., gender) to one-sixth of another (e.g., race) maintains average predictions for subgroups while correcting for the primary attribute.
• Numerical experiments show that the method maintains high predictive performance (F1 ≈ 0.95 on Adult) while significantly reducing unfairness across all tested datasets.
• The sequential framework allows clear interpretation of subgroup-level fairness effects, revealing that correction order can lead to net gains or losses for specific subgroups depending on the sequence.

Figure 2: (Risk, Unfairness) phase diagrams that shows the sequential fairness approach for ( left ) two and ( right ) three sensitive features. In this study, Unfairness represents the overall unfairness $\hat{\mathcal{U}}=\hat{\mathcal{U}}_{1:3}$ . Bottom-left corner gives the best trade-off.