Related papers: The entropic optimal (self-)transport problem: Lim…
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…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
An optimal control problem in the space of Borel measures governed by the Poisson equation is investigated. The characteristic feature of the problem under consideration is the Tikhonov regularization term in form of the transportation…
This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the…
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
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…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…
We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions…
We study an entropic optimal transport problem in which the transport plan is penalized by a nonlinear convex functional acting on the coupling. We establish existence, uniqueness, and uniform a priori bounds for minimizers, and we show…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Classical entropy regularization is poorly suited to continuous-time martingale transport, since relative entropy between diffusion laws typically forces their volatility characteristics to coincide. We introduce a specific-entropy…
Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…