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標(biāo)題: Titlebook: An Invitation to Statistics in Wasserstein Space; Victor M. Panaretos,Yoav Zemel Book‘‘‘‘‘‘‘‘ 2020 The Editor(s) (if applicable) and The A [打印本頁]

作者: 是英寸    時(shí)間: 2025-3-21 18:52
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作者: ALERT    時(shí)間: 2025-3-21 23:29

作者: 編輯才信任    時(shí)間: 2025-3-22 04:20
,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).
作者: PAEAN    時(shí)間: 2025-3-22 08:19
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.
作者: 獎(jiǎng)牌    時(shí)間: 2025-3-22 09:56
,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).
作者: FLAT    時(shí)間: 2025-3-22 13:36
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
作者: 混合,攙雜    時(shí)間: 2025-3-22 18:29
https://doi.org/10.1007/978-3-030-38438-8Optimal Transportation; Monge-Kantorovich Problem; Barycenter; Multimarginal Transport; Functional Data
作者: ovation    時(shí)間: 2025-3-22 21:24

作者: arousal    時(shí)間: 2025-3-23 03:21

作者: Admonish    時(shí)間: 2025-3-23 07:47

作者: Musculoskeletal    時(shí)間: 2025-3-23 13:36
,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.
作者: 解脫    時(shí)間: 2025-3-23 16:49
,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.
作者: 興奮過度    時(shí)間: 2025-3-23 20:16
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.
作者: 物種起源    時(shí)間: 2025-3-24 01:34

作者: Asparagus    時(shí)間: 2025-3-24 03:35
,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.
作者: 分期付款    時(shí)間: 2025-3-24 08:58
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
作者: Nerve-Block    時(shí)間: 2025-3-24 11:44

作者: mutineer    時(shí)間: 2025-3-24 18:45

作者: 缺陷    時(shí)間: 2025-3-24 20:09
,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
作者: Harbor    時(shí)間: 2025-3-25 02:12
,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
作者: 圓錐    時(shí)間: 2025-3-25 03:57
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.
作者: 踉蹌    時(shí)間: 2025-3-25 09:17
The Wasserstein Space,. 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
作者: Mercurial    時(shí)間: 2025-3-25 14:22

作者: gangrene    時(shí)間: 2025-3-25 19:16
2365-4333 infinite dimensional?traits of functional data, but are intrinsically nonlinear due to positivity and?integrability restrictions. Indeed, their dominating statistical variation?arises through random deformatio978-3-030-38437-1978-3-030-38438-8Series ISSN 2365-4333 Series E-ISSN 2365-4341
作者: 暖昧關(guān)系    時(shí)間: 2025-3-25 21:12
Book‘‘‘‘‘‘‘‘ 2020sures on Euclidean space (e.g. images?and point processes). Such random measures carry the infinite dimensional?traits of functional data, but are intrinsically nonlinear due to positivity and?integrability restrictions. Indeed, their dominating statistical variation?arises through random deformatio
作者: Delirium    時(shí)間: 2025-3-26 01:04
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