Computational optimal transport: With applications to data science
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
Statistical aspects of Wasserstein distances
VM Panaretos, Y Zemel - Annual review of statistics and its …, 2019 - annualreviews.org
Wasserstein distances are metrics on probability distributions inspired by the problem of
optimal mass transportation. Roughly speaking, they measure the minimal effort required to …
optimal mass transportation. Roughly speaking, they measure the minimal effort required to …
Iterative Bregman projections for regularized transportation problems
This paper details a general numerical framework to approximate solutions to linear
programs related to optimal transport. The general idea is to introduce an entropic …
programs related to optimal transport. The general idea is to introduce an entropic …
Barycenters in the Wasserstein space
M Agueh, G Carlier - SIAM Journal on Mathematical Analysis, 2011 - SIAM
In this paper, we introduce a notion of barycenter in the Wasserstein space which
generalizes McCann's interpolation to the case of more than two measures. We provide …
generalizes McCann's interpolation to the case of more than two measures. We provide …
[图书][B] Optimal transport: old and new
C Villani - 2009 - Springer
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …
John Mather launched a revolution in the venerable field of optimal transport founded by G …
Wasserstein barycenter and its application to texture mixing
This paper proposes a new definition of the averaging of discrete probability distributions as
a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time …
a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time …
Mathematical risk analysis
L Rüschendorf - Springer Ser. Oper. Res. Financ. Eng. Springer …, 2013 - Springer
This book gives an introduction to basic concepts and methods in mathematical risk
analysis, in particular to those parts of risk theory which are of particular relevance in finance …
analysis, in particular to those parts of risk theory which are of particular relevance in finance …
A Wasserstein-type distance in the space of Gaussian mixture models
J Delon, A Desolneux - SIAM Journal on Imaging Sciences, 2020 - SIAM
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture
models. This distance is defined by restricting the set of possible coupling measures in the …
models. This distance is defined by restricting the set of possible coupling measures in the …
Regularized discrete optimal transport
This article introduces a generalization of the discrete optimal transport, with applications to
color image manipulations. This new formulation includes a relaxation of the mass …
color image manipulations. This new formulation includes a relaxation of the mass …
An optimal transport approach for the Schrödinger bridge problem and convergence of Sinkhorn algorithm
This paper exploit the equivalence between the Schrödinger Bridge problem (Léonard in J
Funct Anal 262: 1879–1920, 2012; Nelson in Phys Rev 150: 1079, 1966; Schrödinger in …
Funct Anal 262: 1879–1920, 2012; Nelson in Phys Rev 150: 1079, 1966; Schrödinger in …