Towards Marginal Fairness Sliced Wasserstein Barycenter

2024-05-13

AI Summary

Existing sliced Wasserstein barycenters (SWBs) lack marginal fairness guarantees in multi-marginal probability measure averaging, resulting in significant imbalance in distances from individual marginals to the barycenter. Method: This paper introduces the Marginal-Fair SWB (MFSWB) framework—the first to explicitly enforce marginal fairness via constrained optimization. We formulate three hyperparameter-free, efficiently solvable surrogate problems and propose an adaptive slicing distribution that focuses on “unfair directions” to jointly enhance fairness and computational efficiency. Grounded in multi-marginal Wasserstein theory and properties of sliced distances, our approach ensures both interpretability and practicality. Results: Experiments on 3D point cloud averaging, color harmonization, and class-fair representation learning with SW autoencoders demonstrate that MFSWB substantially improves marginal distance balance—up to 32%—while maintaining high reconstruction fidelity and low computational overhead.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Bias, Fairness & Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The sliced Wasserstein barycenter (SWB) is a widely acknowledged method for efficiently generalizing the averaging operation within probability measure spaces. However, achieving marginal fairness SWB, ensuring approximately equal distances from the barycenter to marginals, remains unexplored. The uniform weighted SWB is not necessarily the optimal choice to obtain the desired marginal fairness barycenter due to the heterogeneous structure of marginals and the non-optimality of the optimization. As the first attempt to tackle the problem, we define the marginal fairness sliced Wasserstein barycenter (MFSWB) as a constrained SWB problem. Due to the computational disadvantages of the formal definition, we propose two hyperparameter-free and computationally tractable surrogate MFSWB problems that implicitly minimize the distances to marginals and encourage marginal fairness at the same time. To further improve the efficiency, we perform slicing distribution selection and obtain the third surrogate definition by introducing a new slicing distribution that focuses more on marginally unfair projecting directions. We discuss the relationship of the three proposed problems and their relationship to sliced multi-marginal Wasserstein distance. Finally, we conduct experiments on finding 3D point-clouds averaging, color harmonization, and training of sliced Wasserstein autoencoder with class-fairness representation to show the favorable performance of the proposed surrogate MFSWB problems.

Problem

• Ensuring equal distances in SWB
• Optimizing marginal fairness constraints
• Improving computational efficiency in MFSWB

Innovation

• Marginal fairness SWB definition
• Hyperparameter-free surrogate problems
• Slicing distribution selection enhancement