相关论文: Dynamic Models of Wasserstein-1-Type Unbalanced Tr…

Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…

After presenting an overview about variational problems on probability measures for functionals involving transport costs and extra terms encouraging or discouraging concentration, we look for optimality conditions, regularity properties…

We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…

In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the…

We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical…

Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such…

Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…

In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…

We introduce dynamic and static formulations that formally extend unbalanced optimal transport from the space of positive densities to the space of Riemannian metrics. The first construction is based on a dynamic variational formulation in…

We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…

The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…

This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…

Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…

This paper presents a decentralized control framework for distribution matching in multi-agent systems (MAS), where agents collectively achieve a prescribed terminal spatial distribution. The problem is formulated using optimal transport…

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…

We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a…

The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…

Optimal transport has gained much attention in image processing field, such as computer vision, image interpolation and medical image registration. Recently, Bredies et al. (ESAIM:M2AN 54:2351-2382, 2020) and Schmitzer et al. (IEEE T MED…

Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…