论文标题
Wasserstein空间中的统计学习
Statistical learning in Wasserstein space
论文作者
论文摘要
我们寻求对数据点由Wasserstein度量分布进行分布的度量空间中回归和原理分析（PCA）的概括。我们将这些分析作为多边缘最佳运输问题进行了重新铸造。特定的公式允许有效的计算，确保存在最佳解决方案，并在路径空间（线段）上接受概率解释。设想了该理论在经验分布，图像，功率谱以及评估实验设计中的不确定性的插值中的应用。
We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems. The particular formulation allows efficient computation, ensures existence of optimal solutions, and admits a probabilistic interpretation over the space of paths (line segments). Application of the theory to the interpolation of empirical distributions, images, power spectra, as well as assessing uncertainty in experimental designs, is envisioned.
