Related papers: Non-commutative Optimal Transport for semi-definit…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
We study the convergence of the transport plans $\gamma_\epsilon$ towards $\gamma_0$ as well as the cost of the entropy-regularized optimal transport $(c,\gamma_\epsilon)$ towards $(c,\gamma_0)$ as the regularization parameter $\epsilon$…
Solving large scale entropic optimal transport problems with the Sinkhorn algorithm remains challenging, and domain decomposition has been shown to be an efficient strategy for problems on large grids. Unbalanced optimal transport is a…
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…
This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…
Optimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positive (probability) measures and therefore strategies are…
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…
Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…
Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Brenier's theorem and the Kantorovich-Rubinstein formula are…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to…