Titlebook: An Invitation to Statistics in Wasserstein Space; Victor M. Panaretos,Yoav Zemel Book‘‘‘‘‘‘‘‘ 2020 The Editor(s) (if applicable) and The A

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,Der Petroleum-Tankdampfer ?August Korff?,stein space .. It reduces the problem of finding the Fréchet mean to a succession of pairwise transport problems, involving only the Monge–Kantorovich problem between two measures. In the Gaussian case (or any location-scatter family), the latter can be done explicitly, rendering the algorithm particularly appealing (see Sect. 5.4.1).

PAEAN

The Wasserstein Space,r some basic definitions, we describe the topological properties of that space in Sect. 2.2. It is then explained in Sect. 2.3 how . can be endowed with a sort of infinite-dimensional Riemannian structure. Measurability issues are dealt with in the somewhat technical Sect. 2.4.

獎(jiǎng)牌

,Construction of Fréchet Means and Multicouplings,stein space .. It reduces the problem of finding the Fréchet mean to a succession of pairwise transport problems, involving only the Monge–Kantorovich problem between two measures. In the Gaussian case (or any location-scatter family), the latter can be done explicitly, rendering the algorithm particularly appealing (see Sect. 5.4.1).

FLAT

2365-4333 hematical literature.Presents an up-to-date overview of the .This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspect

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https://doi.org/10.1007/978-3-030-38438-8Optimal Transportation; Monge-Kantorovich Problem; Barycenter; Multimarginal Transport; Functional Data

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