Related papers: Empirical Regularized Optimal Transport: Statistic…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
A new data-enabled control technique for uncertain linear time-invariant systems, recently conceived by Coulson et\ al., builds upon the direct optimization of controllers over input/output pairs drawn from a large dataset. We adopt an…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
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…
In this paper we determine quantitative stability bounds for the Hessian of entropic potentials, \ie, the dual solution to the entropic optimal transport problem. To the authors' knowledge this is the first work addressing this second-order…
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measured in Wasserstein distance, which are applicable to a wide…
This paper studies the convergence rates of optimal transport (OT) map estimators, a topic of growing interest in statistics, machine learning, and various scientific fields. Despite recent advancements, existing results rely on regularity…
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…
Beckmann's problem in optimal transport minimizes the total squared flux in a continuous transport problem from a source to a target distribution. In this article, the regularity theory for solutions to Beckmann's problem in optimal…
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
In modern experimental science, there is a common problem of estimating the coefficients of a linear regression in a context where the variables of interest cannot be observed simultaneously. When there is a categorical variable that is…
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…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
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 prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…
We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to…
In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex…