Multi-marginal Wasserstein GAN

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.

Authors

• Jiezhang Cao Harvard University
• Langyuan Mo
• Yifan Zhang School of Computer Science, Peking University MoE Key Lab. of High Confidence Software Technologies(PKU), China
• Kui Jia School of Data Science, The Chinese University of Hong Kong, Shenzhen
• Chunhua Shen College of Computer Science and Technology, Zhejiang University
• Mingkui Tan South China University of Technology

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