Related papers: Uniform optimal-order Wasserstein quantisation
In this paper we study the BV regularity for solutions of variational problems in Optimal Transportation. As an application we recover BV estimates for solutions of some non-linear parabolic PDE by means of optimal transportation…
Given a real number $\alpha \in (0,1)$, we define the Webster sequence of density $\alpha$ to be $W_\alpha = (\lceil(n-1/2) / \alpha\rceil)_{n\in\mathbb{N}}$, where $\lceil x \rceil$ is the ceiling function. It is known that if $\alpha$ and…
This paper studies a combined space partitioning and network flow optimization problem, with applications to large-scale power, transportation, or communication systems. In dense wireless networks, one may want to simultaneously optimize…
We introduce a one-parameter family of metrics on the space of Borel probability measures on Euclidean space with finite $p$th moment for $1\leq p <\infty$, called the $\textit{sliced Monge--Kantorovich metrics}$, which include the sliced…
This study examines the time complexities of the unbalanced optimal transport problems from an algorithmic perspective for the first time. We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently.…
Given a determinate (multivariate) probability measure $\mu$, we characterize Gaussian mixtures $\nu\_\phi$ which minimize the Wasserstein distance $W\_2(\mu,\nu\_\phi)$ to $\mu$ when the mixing probability measure $\phi$ on the parameters…
We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…
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…
Gr\"unbaum's equipartition problem asked if for any measure $\mu$ on $\mathbb{R}^d$ there are always $d$ hyperplanes which divide $\mathbb{R}^d$ into $2^d$ $\mu$-equal parts. This problem is known to have a positive answer for $d\le 3$ and…
We introduce a constrained optimal transport problem where origins $x$ can only be transported to destinations $y\geq x$. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect $Y-X$ given…
We study approximate distributed solutions to the weighted {\it all-pairs-shortest-paths} (APSP) problem in the CONGEST model. We obtain the following results. $1.$ A deterministic $(1+o(1))$-approximation to APSP in $\tilde{O}(n)$ rounds.…
We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path-length $s$), and models particle transport…
We address the problem of proving a Central Limit Theorem for the empirical optimal transport cost, $\sqrt{n}\{\mathcal{T}_c(P_n,Q)-\mathcal{W}_c(P,Q)\}$, in the semi discrete case, i.e when the distribution $P$ is finitely supported. We…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
When quantum teleportation is performed with truly identical massive particles, indistinguishability allows us to teleport addressable degrees of freedom which do not identify particles, but e.g. orthogonal modes. The key resource of the…
Barycenter problems encode important geometric information about a metric space. While these problems are typically studied with positive weight coefficients associated to each distance term, more general signed Wasserstein barycenter…
A 1-factorisation of a regular graph $G$ is a partition of its edge set $E(G)$ into perfect matchings of $G$. Behague asked for the minimal $r=r(d)$ such that some $1$-factorisation of the $d$-dimensional hypercube $Q_d$ has the property…
The Wasserstein distance provides a notion of dissimilarities between probability measures, which has recent applications in learning of structured data with varying size such as images and text documents. In this work, we study the…