Related papers: Rethinking Initialization of the Sinkhorn Algorith…
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…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…
We present a new approach for Neural Optimal Transport (NOT) training procedure, capable of accurately and efficiently estimating optimal transportation plan via specific regularization on dual Kantorovich potentials. The main bottleneck of…
Recently, Sinkhorn's algorithm was applied for approximately solving linear programs emerging from optimal transport very efficiently. This was accomplished by formulating a regularized version of the linear program as Bregman projection…
Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…
In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown…
In this paper, we study the Entropic Martingale Optimal Transport (EMOT) problem on \mathbb{R}. The investigation of the EMOT problem arises in the calibration problem of the Stochastic Volatility Models, where martingale constraints…
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast…
Vector quantile regression (VQR) is an optimal transport (OT)-based framework that extends linear quantile regression to vector-valued response variables and can be formulated as an OT problem with a mean-independence constraint. In this…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
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…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
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…
Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. Recent works suggest that these estimators are more statistically efficient than plug-in (linear…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost $c(x,y)=\|x-y\|$ in dimension $d>1$. We develop a comprehensive variational convergence framework that entails…
Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of geodesics in the group of measure-preserving diffeomorphisms, we propose a numerical method based on Sinkhorn's algorithm for the entropic…
Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…