Related papers: Uniform optimal-order Wasserstein quantisation
We introduce folded optimal transport, as a method to extend a cost or distance defined on the extreme boundary of a convex to the whole convex, related to convex extension. This construction broadens the framework of standard optimal…
Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform,…
In this work, we present a method to compute the Kantorovich-Wasserstein distance of order one between a pair of two-dimensional histograms. Recent works in Computer Vision and Machine Learning have shown the benefits of measuring…
A data-driven formulation of the optimal transport problem is presented and solved using adaptively refined meshes to decompose the problem into a sequence of finite linear programming problems. Both the marginal distributions and their…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where…
We study the Bergman determinantal point process from a theoretical point of view motivated by its simulation. We construct restricted and restricted-truncated variants of the Bergman kernel and show optimal transport inequalities involving…
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost. Our proposal is the first where the transport…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
We discuss a phenomenon where Optimal Transport leads to a remarkable amount of combinatorial regularity. Consider infinite sequences $(x_k)_{k=1}^{\infty}$ in $[0,1]$ constructed in a greedy manner: given $x_1, \dots, x_n$, the new point…
The assignment problem, a cornerstone of operations research, seeks an optimal one-to-one mapping between agents and tasks to minimize total cost. This work traces its evolution from classical formulations and algorithms to modern optimal…
We introduce the optimal transportation interpretation of the Kantorovich norm on thespace of signed Radon measures with finite mass, based on a generalized Wasserstein distancefor measures with different masses.With the formulation and the…
We study the optimal transport problem in sub-Riemannian manifolds where the cost function is given by the square of the sub-Riemannian distance. Under appropriate assumptions, we generalize Brenier-McCann's Theorem proving existence and…
In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization…
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…
We consider the problem of optimal incomplete transportation between the empirical measure on an i.i.d. uniform sample on the d-dimensional unit cube $[0,1]^d$ and the true measure. This is a family of problems lying in between classical…
We introduce quantum optimal transport of states on tracial AF-$C^{*}$-algebras to study non-spatial transport of quantum information, and view it as the pointwise case of a general parametrised one. We define quantum optimal transport…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
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.…