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

Musculoskeletal

,Fréchet Means in the Wasserstein Space ,,If . is a Hilbert space (or a closed convex subspace thereof) and .., …, .. ∈ ., then the empirical mean . is the unique element of . that minimises the sum of squared distances from the ..’s.

解脱

,Phase Variation and Fréchet Means,Why is it relevant to construct the Fréchet mean of a collection of measures with respect to the Wasserstein metric? A simple answer is that this kind of average will often express a more natural notion of “typical” realisation of a random probability distribution than an arithmetic average.

兴奋过度

Optimal Transport, this topic are the books by Rachev and Rüschendorf [.], Villani [., .], Ambrosio et al. [.], Ambrosio and Gigli [.], and Santambrogio [.]. This chapter includes only few proofs, when they are simple, informative, or are not easily found in one of the cited references.

物种起源

Asparagus

,Der Petroleum-Tankdampfer »August Korff«, this topic are the books by Rachev and Rüschendorf [.], Villani [., .], Ambrosio et al. [.], Ambrosio and Gigli [.], and Santambrogio [.]. This chapter includes only few proofs, when they are simple, informative, or are not easily found in one of the cited references.

分期付款

Victor M. Panaretos,Yoav ZemelGives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature.Presents an up-to-date overview of the

Nerve-Block

mutineer

缺陷

,Die Kaiseryacht »Hohenzollern«,. The resulting metric space, a subspace of ., is commonly known as the . . (although, as Villani [., pages 118–119] puts it, this terminology is “very questionable”; see also Bobkov and Ledoux [., page 4]). In Chap. ., we shall see that this metric is in a sense canonical when dealing with warpings

Harbor

,Der Petroleum-Tankdampfer »August Korff«,multivariate case, where, apart from the important yet special case of compatible measures, closed-form formulae are not available. This chapter presents an iterative procedure that provably approximates at least a Karcher mean with mild restrictions on the measures .., …, ... The algorithm is based