Related papers: Entropic estimation of optimal transport maps
We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr\"odinger potentials describing the density of the optimal…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
We develop a general approach to prove global regularity estimates for quadratic optimal transport using the entropic regularisation of the problem and the Prekopa-Leindler inequality.
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
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…
Optimal transport is a powerful framework for computing distances between probability distributions. We unify the two main approaches to optimal transport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define as Tsallis…
We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $\mu$ and $\nu$. Our work is motivated by the specific setting of Monge-Kantorovich quantiles where…
In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…
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…
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…
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…
Estimating optimal transport (OT) maps (a.k.a. Monge maps) between two measures $P$ and $Q$ is a problem fraught with computational and statistical challenges. A promising approach lies in using the dual potential functions obtained when…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
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.…