Related papers: Knothe-Rosenblatt maps via soft-constrained optima…
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…
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…
Bi-causal optimal transport (OT) is a natural framework for comparing and coupling stochastic processes under nonanticipative information constraints, with important applications in robust finance, sequential uncertainty quantification, and…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
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…
The optimal transport problem studies how to transport one measure to another in the most cost-effective way and has wide range of applications from economics to machine learning. In this paper, we introduce and study an information…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
For two probability measures $\rho$ and $\pi$ on $[-1,1]^{\mathbb{N}}$ we investigate the approximation of the triangular Knothe-Rosenblatt transport $T:[-1,1]^{\mathbb{N}}\to [-1,1]^{\mathbb{N}}$ that pushes forward $\rho$ to $\pi$. Under…
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…
We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…
We study estimators of the optimal transport (OT) map between two probability distributions. We focus on plugin estimators derived from the OT map between estimates of the underlying distributions. We develop novel stability bounds for OT…
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…
Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in…
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…