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 …
Wasserstein distributionally robust optimization: Theory and applications in machine learning
Many decision problems in science, engineering, and economics are affected by uncertain
parameters whose distribution is only indirectly observable through samples. The goal of …
parameters whose distribution is only indirectly observable through samples. The goal of …
Smooth and sparse optimal transport
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It
enables to cast the OT computation as a differentiable and unconstrained convex …
enables to cast the OT computation as a differentiable and unconstrained convex …
When optimal transport meets information geometry
G Khan, J Zhang - Information Geometry, 2022 - Springer
Abstract Information geometry and optimal transport are two distinct geometric frameworks
for modeling families of probability measures. During the recent years, there has been a …
for modeling families of probability measures. During the recent years, there has been a …
Sinkhorn autoencoders
Optimal transport offers an alternative to maximum likelihood for learning generative
autoencoding models. We show that minimizing the $ p $-Wasserstein distance between the …
autoencoding models. We show that minimizing the $ p $-Wasserstein distance between the …
Polynomial-time algorithms for multimarginal optimal transport problems with structure
JM Altschuler, E Boix-Adsera - Mathematical Programming, 2023 - Springer
Abstract Multimarginal Optimal Transport (MOT) has attracted significant interest due to
applications in machine learning, statistics, and the sciences. However, in most applications …
applications in machine learning, statistics, and the sciences. However, in most applications …
Regularized optimal transport and the rot mover's distance
This paper presents a unified framework for smooth convex regularization of discrete optimal
transport problems. In this context, the regularized optimal transport turns out to be …
transport problems. In this context, the regularized optimal transport turns out to be …
[PDF][PDF] Scalable computation of monge maps with general costs
Monge map refers to the optimal transport map between two probability distributions and
provides a principled approach to transform one distribution to another. In spite of the rapid …
provides a principled approach to transform one distribution to another. In spite of the rapid …
Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem
Two geometrical structures have been extensively studied for a manifold of probability
distributions. One is based on the Fisher information metric, which is invariant under …
distributions. One is based on the Fisher information metric, which is invariant under …
Learning to match via inverse optimal transport
We propose a unified data-driven framework based on inverse optimal transport that can
learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical …
learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical …