Towards Marginal Fairness Sliced Wasserstein Barycenter
Khai Nguyen, Hai Nguyen, Nhat Ho
TL;DR
This paper introduces a novel approach to achieve marginal fairness in sliced Wasserstein barycenters by defining a constrained problem and proposing computationally efficient surrogate solutions, validated through diverse experiments.
Contribution
It is the first to define marginal fairness sliced Wasserstein barycenter and proposes three surrogate problems that are hyperparameter-free and computationally tractable.
Findings
Surrogate MFSWB effectively improves marginal fairness.
Proposed methods perform well in 3D point-cloud averaging.
Applications include color harmonization and fair autoencoder training.
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…
Peer Reviews
Decision·ICLR 2025 Spotlight
This paper addresses an important problem that has been overlooked. In traditional SWB, the weights between barycenter and marginals are uniform. However, this uniform weights actually leads to non-uniform distances between the barycenter and the marginals. The authors have a simple experiment demonstrating that in the paper. To ensure equal distances, they propose the MFSWB to address this problem. They define MFSWB such that the average distance to be within an $\epsilon$. The proposed MFSWB
I didn't really catch any weakness of this paper. The paper is complete with clear motivation, effective solutions and sufficient experimental results.
1. The paper is well-organized and the writing is good. 2. The paper has solid theoretical proofs. 3. The story line is easy to follow.
Please refer to questions.
- The presented problem is novel and reasonable. If fairness of barycenter can be achieved w.r.t. marginals, then varous future applicaiton can be conducted e.g. ensuring fairness of ML algorithms. - The paper organization, problem definition and writing is good and easy to follow. If audience has some Sliced Wasserstein knowledge, then it will be easy to follow the idea. - The Lagaragian formulation as well as three surrogates are proposed to deal with the Fairness barycenter estimation with
- Most of the experiments conducted are simple or on simple dataset, such as Gaussian, Simple Color Hamonization of two images or point cloud of only two shapes, AE on simple MNIST dataset. I am wondering the scability and real application of the proposed method. For example, if more than two (e.g. >5) images or point clouds are adopted, what might be the results? Or are there more realistic potential appplications of the proposed method? If related work or potential applications are discu
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Taxonomy
TopicsGenerative Adversarial Networks and Image Synthesis · 3D Shape Modeling and Analysis · Adversarial Robustness in Machine Learning