论文标题
合作运输
CO-Optimal Transport
论文作者
论文摘要
最佳传输（OT）是一种强大的几何和概率工具，用于查找两个分布之间的相似性并测量相似性。然而，其原始配方依赖于两个分布的样品之间的成本函数的存在，这使得它们在不同空间上受支持时变得不切实际。为了规避这一限制，我们提出了一个新的OT问题，名为COOT，以合作运输为名，该问题同时优化了两个样品和特征之间的两个运输图，与其他方法相反，这些方法要么通过将单个特征集中在样品之间的成对距离上，要么需要明确地模型它们之间的关系。我们对问题进行了彻底的理论分析，建立了与其他基于OT的距离的丰富联系，并证明了其在异质域适应性和共聚类/数据摘要中的两个机器学习应用程序的多功能性，其中COOT会导致对最新方法的性能提高。
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the samples of the two distributions, which makes it impractical when they are supported on different spaces. To circumvent this limitation, we propose a novel OT problem, named COOT for CO-Optimal Transport, that simultaneously optimizes two transport maps between both samples and features, contrary to other approaches that either discard the individual features by focusing on pairwise distances between samples or need to model explicitly the relations between them. We provide a thorough theoretical analysis of our problem, establish its rich connections with other OT-based distances and demonstrate its versatility with two machine learning applications in heterogeneous domain adaptation and co-clustering/data summarization, where COOT leads to performance improvements over the state-of-the-art methods.
