The Monge–Kantorovich Mass Transference Problem and Its Stochastic Applications

By Svetlozar T. Rachev. 1985

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Citations in the corpus

On the empirical estimation of integral probability metrics (2012, methodology): “IPMs have been employed as tools of theoretical interest in probability theory [15, Chapter 11], with applications including mass transportation problems [34] and empirical process theory [50].”
On integral probability metrics, φ-divergences and binary classification (2009, neutral): “II.”
Large Scale Fine-Grained Categorization and Domain-Specific Transfer Learning (2018, methodology): “3 illustrates calculating the proposed domain similarity by EMD.”
Existence and uniqueness of monotone measure-preserving maps (1995, background): “associated Monge-Kantorovich mass transport problem (see, e.g., [ 15 ]).”
Probability distance inequalities on Riemannian manifolds and path spaces (2004, methodology): “p (f„;„) as n ! 1, see e.g. [ 16 ]. Therefore, in the proof of”
Bounds on the constant in the mean central limit theorem (2009, unknown): “jjF Gjj1 = EjF 1(U) G 1(U)j; (18) see [ 14 ] for details.”
On the Monge mass transfer problem (2001, background): “For further discussion on the Monge problem, and its interesting history and various applications, the reader is referred for example to [5, 7, 8, 10, 14, 17].”
Shape matching: similarity measures and algorithms (2001, methodology): “The transport distance has been used in heat transform problems [43], object contour matching [19], and color-based image retrieval [46].”
Inference for empirical Wasserstein distances on finite spaces (2016, background): “…known as the Mallows distance (Mallows, 1972), the Monge–Kantorovich–Rubinstein distance in the physical sciences (Kantorovich and Rubinstein, 1958; Rachev, 1985; Jordan et al., 1998), the earth mover’s distance in computer science (Rubner et al., 2000) or the optimal transport distance in…”
The Earth Mover's distance is the Mallows distance: some insights from statistics (2001, background): “It was introduced in the statistical literature in 1972 by [7], but it had also independently appeared a little earlier in the physics and probability literatures, and some date it all the way back to the 1940s [10].”
Duality and existence for a class of mass transportation problems and economic applications (2003, background): “The problem of optimal measure preserving maps (M) has received a lot of attention since related questions naturally arise in fluid mechanics [2], differential geometry (see [16] for relation with a classical result of Aleksandrov [1]), shape optimization [4] , functional analysis [11], [12], probab”
Statistical Aspects of Wasserstein Distances (2018, background): “In addition to the survey Rachev (1985), there are a number of books dedicated to optimal transport: Rachev & R¨uschendorf (1998), Villani (2003, 2008), Am-brosio & Gigli (2013), Santambrogio (2015), and the forthcoming Panaretos & Zemel (in review), leaning to the statistical side of the subject.”