Multi-marginal Wasserstein GAN
This addresses multi-domain matching challenges for applications like image translation, but appears incremental as it builds on existing GAN and optimal transport frameworks.
The paper tackles the problem of learning mappings to match a source domain to multiple target domains, such as in multi-domain image translation, by proposing Multi-marginal Wasserstein GAN (MWGAN) to minimize Wasserstein distance among domains, with experiments on toy and real-world datasets demonstrating its effectiveness.
Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this problem has two critical challenges: (i) Measuring the multi-marginal distance among different domains is very intractable; (ii) It is very difficult to exploit cross-domain correlations to match the target domain distributions. In this paper, we propose a novel Multi-marginal Wasserstein GAN (MWGAN) to minimize Wasserstein distance among domains. Specifically, with the help of multi-marginal optimal transport theory, we develop a new adversarial objective function with inner- and inter-domain constraints to exploit cross-domain correlations. Moreover, we theoretically analyze the generalization performance of MWGAN, and empirically evaluate it on the balanced and imbalanced translation tasks. Extensive experiments on toy and real-world datasets demonstrate the effectiveness of MWGAN.