Results 71 to 80 of about 2,509,053 (235)
On Properties of the Generalized Wasserstein Distance [PDF]
Archive for Rational Mechanics and Analysis, 2016 The Wasserstein distances $W_p$ ($p\geq 1$), defined in terms of solution to the Monge-Kantorovich problem, are known to be a useful tool to investigate transport equations. In particular, the Benamou-Brenier formula characterizes the square of the Wasserstein distance $W_2$ as the infimum of the kinetic energy, or action functional, of all vector ...
Piccoli, Benedetto, Rossi, Francesco
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The Gromov–Wasserstein Distance: A Brief Overview
Axioms, 2014 We recall the construction of the Gromov–Wasserstein distance and concentrate on quantitative aspects of the definition.
Facundo Mémoli
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The Quantum Wasserstein Distance of Order 1 [PDF]
IEEE Transactions on Information Theory, 2020 We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance for quantum ...
Giacomo De Palma +3 more
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Irregularity of Distribution in Wasserstein Distance [PDF]
Journal of Fourier Analysis and Applications, 2020 We study the non-uniformity of probability measures on the interval and the circle. On the interval, we identify the Wasserstein-$p$ distance with the classical $L^p$-discrepancy. We thereby derive sharp estimates in Wasserstein distances for the irregularity of distribution of sequences on the interval and the circle.
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Scalar conservation laws seen as gradient flows: known results and new perspectives
ESAIM: Proceedings and Surveys, 2016 We review some results in the literature which attempted (only partly successfully) at linking the theory of scalar conservation laws with the Wasserstein gradient flow theory.
Di Francesco Marco
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Towards Inverse Modeling of Landscapes Using the Wasserstein Distance
Geophysical Research Letters, 2023 Extricating histories of uplift and erosion from landscapes is crucial for many branches of the Earth sciences. An objective way to calculate such histories is to identify calibrated models that minimize misfit between observations (e.g., topography) and
M. J. Morris, A. G. Lipp, G. G. Roberts
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Basic statistics for probabilistic symbolic variables: a novel metric-based approach
, 2013 In data mining, it is usually to describe a set of individuals using some summaries (means, standard deviations, histograms, confidence intervals) that generalize individual descriptions into a typology description. In this case, data can be described by
Irpino, Antonio, Verde, Rosanna
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High-Dimensional Distributionally Robust Mean-Variance Efficient Portfolio Selection
Mathematics, 2023 This paper introduces a novel distributionally robust mean-variance portfolio estimator based on the projection robust Wasserstein (PRW) distance. This approach addresses the issue of increasing conservatism of portfolio allocation strategies due to high-
Zhonghui Zhang, Huarui Jing, Chihwa Kao
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Wasserstein distance, Fourier series and applications [PDF]
Monatshefte für Mathematik, 2021 We study the Wasserstein metric $W_p$, a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance $W_1$ between the distribution of quadratic residues in a finite field $\mathbb{F}_p$ and uniform distribution by $\lesssim p^{-1/2}$ (the ...
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Advanced Intelligent Discovery, EarlyView.We investigate MACE‐MP‐0 and M3GNet, two general‐purpose machine learning potentials, in materials discovery and find that both generally yield reliable predictions. At the same time, both potentials show a bias towards overstabilizing high energy metastable states. We deduce a metric to quantify when these potentials are safe to use.
Konstantin S. Jakob +2 more
wiley +1 more source