Statistical Learning in Wasserstein Space
Statistical Learning in Wasserstein Space
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DOI：
10.1109/lcsys.2020.3006965
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发表时间：
2021-07-01
影响因子：
3
通讯作者：
Georgiou, Tryphon T.
中科院分区：
文献类型：
--
作者：
Karimi, Amirhossein;Ripani, Luigia;Georgiou, Tryphon T.
我们寻求回归和主成分分析（PCA）在度量空间中的数据点的分布度量的Wasserstein度量的泛化。我们将这些分析转化为多边际最优运输问题。特定的配方允许有效的计算，确保最优解的存在，并承认在路径（线段）空间的概率解释。应用该理论的插值经验分布，图像，功率谱，以及评估实验设计中的不确定性，设想。
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.