Related papers: E-ROBOT: a dimension-free method for robust statis…
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…
The Sinkhorn--Knopp (SK) algorithm is a cornerstone method for matrix scaling and entropically regularized optimal transport (EOT). Despite its empirical efficiency, existing theoretical guarantees to achieve a target marginal accuracy…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…
Entropy-regularized optimal transport, which has strong links to the Schr\"odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed…
The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…
The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent…
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…
Data-driven Distributionally Robust Optimization (DD-DRO) via optimal transport has been shown to encompass a wide range of popular machine learning algorithms. The distributional uncertainty size is often shown to correspond to the…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT problem, the entropic OT problem, which allows to implement…
Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can…
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…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…
Entropic regularization provides a simple way to approximate linear programs whose constraints split into two or more tractable blocks. The resulting objectives are amenable to cyclic Kullback-Leibler (KL) Bregman projections, with…
In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schr\"odinger bridge problem by penalizing the transport…
Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…