Second-Order Models for Optimal Transport and Cubic Splines on the Wasserstein Space
Second-Order Models for Optimal Transport and Cubic Splines on the Wasserstein Space
复制标题
Wasserstein 空间上最优传输和三次样条的二阶模型
DOI：
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发表时间：
2018
影响因子：
3
通讯作者：
François
中科院分区：
文献类型：
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作者：
J. Benamou;T. Gallouët;François
在概率密度的空间上，我们将Wasserstein Geodesics扩展到高阶插值的情况，例如立方样条插值。在将立方花纹的自然延伸到瓦斯堡空间中后，我们提出了一种基于路径空间上变异问题的放松的简单方法。我们探讨了两种不同的数值方法，一种基于多边缘最佳运输和熵正则化，另一种基于半差异的最佳运输。
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we propose a simpler approach based on the relaxation of the variational problem on the path space. We explore two different numerical approaches, one based on multimarginal optimal transport and entropic regularization and the other based on semi-discrete optimal transport.