Related papers: An algorithm for optimal transport between a simpl…
We develop a computationally tractable method for estimating the optimal map between two distributions over $\mathbb{R}^d$ with rigorous finite-sample guarantees. Leveraging an entropic version of Brenier's theorem, we show that our…
We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class…
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…
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…
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
Gas transportation and storage has become one of the most relevant and important optimization problems in energy systems. This problem inherently includes highly nonlinear and nonconvex aspects due to gas physics, and discrete aspects due…
We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to a regular (shifted) lattice. The main focus of the article…
We propose a novel algorithm for solving convex, constrained and distributed optimization problems defined on multi-agent-networks, where each agent has exclusive access to a part of the global objective function. The agents are able to…
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…
A numerical method for the solution of the elliptic Monge-Ampere Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem is presented. A local representation of the OT boundary…
We show that, on a $2$-dimensional compact manifold, the optimal transport map in the semi-discrete random matching problem is well-approximated in the $L^2$-norm by identity plus the gradient of the solution to the Poisson problem $-\Delta…
This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson point process. We prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite. Moreover, we give…
Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond. Monotone triangular transport…
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…
We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…
Replacing the quadratic proximal penalty familiar from Hilbert spaces by an unbalanced optimal transport distance, we develop forward-backward type optimisation methods in spaces of Radon measures. We avoid the actual computation of the…
We propose and analyze a modified damped Newton algorithm to solve the semi-discrete optimal transport with storage fees. We prove global linear convergence for a wide range of storage fee functions, the main assumption being that each…
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast…