联合分布匹配（Joint Distribution Matching，JDM）问题是指在机器学习和计算机视觉等应用中，通过学习双向映射来匹配两个域的联合分布的问题。然而，由于两个关键挑战，这个问题非常困难：（i）通常难以利用来自联合分布的足够信息来进行匹配;（ii）这个问题难以公式化和优化。在本文中，依靠最优运输理论，我们提出解决JDM问题的最小化Wasserstein距离的联合分布在两个区域。然而，由此产生的优化问题仍然是棘手的。在此基础上，我们提出了一个重要的定理，将这个复杂的问题转化为一个简单的优化问题，并提出了一种新的方法（称为联合Wasserstein分布匹配（JWDM））来解决这个问题。定性和定量的比较表明，我们的方法优于几个国家的最先进的性能。
英文摘要：
Joint distribution matching (JDM) problem, which aims to learn bidirectional mappings to match joint distributions of two domains, occurs in many machine learning and computer vision applications. This problem, however, is very difficult due to two critical challenges: (i) it is often difficult to exploit sufficient information from the joint distribution to conduct the matching; (ii) this problem is hard to formulate and optimize. In this paper, relying on optimal transport theory, we propose to address JDM problem by minimizing the Wasserstein distance of the joint distributions in two domains. However, the resultant optimization problem is still intractable. We then propose an important theorem to reduce the intractable problem into a simple optimization problem, and develop a novel method (called Joint Wasserstein Distribution Matching (JWDM)) to solve it. In the experiments, we apply our method to unsupervised image translation and cross-domain video synthesis. Both qualitative and quantitative comparisons demonstrate the superior performance of our method over several state-of-the-arts.
The Joint Gromov Wasserstein Objective for Multiple Object Matching
Department of Computer Science, University of British Columbia（不列颠哥伦比亚大学计算机科学系）；Department of Mathematics, University of British Columbia（不列颠哥伦比亚大学数学系）
Joint Cuts and Matching of Partitions in One Graph
Arizona State University（亚利桑那州立大学）；Shanghai Jiao Tong University（上海交通大学）；IBM Research -- China（IBM中国研究院）；University of Texas at Houston（德克萨斯大学休斯顿健康科学中心）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of California, San Diego（加州大学圣地亚哥分校）；National University of Singapore（新加坡国立大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Sri Aurobindo International Centre of Education（斯里阿罗bindo国际教育中心）
