Related papers: Convergence Rates for Regularized Optimal Transpor…
We consider the conjecture proposed in Matsumoto, Zhang and Schiebinger (2022) suggesting that optimal transport with quadratic regularisation can be used to construct a graph whose discrete Laplace operator converges to the…
Computationally solving multi-marginal optimal transport (MOT) with squared Euclidean costs for $N$ discrete probability measures has recently attracted considerable attention, in part because of the correspondence of its solutions with…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the…
In this paper, we address the numerical solution to the multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including…
A common way to quantify the ,,distance'' between measures is via their discrepancy, also known as maximum mean discrepancy (MMD). Discrepancies are related to Sinkhorn divergences $S_\varepsilon$ with appropriate cost functions as…
A recent paper by Cordero-Erausquin and Klartag provides a characterization of the measures $\mu$ on $\R^d$ which can be expressed as the moment measures of suitable convex functions $u$, i.e. are of the form $(\nabla u)\_\\#e^{- u}$ for…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive matrices (not necessarily with trace one). We prove the…
We study stability of optimizers and convergence of Sinkhorn's algorithm for the entropic optimal transport problem. In the special case of the quadratic cost, our stability bounds imply that if one of the two entropic potentials is…
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
The optimal transport problem with quadratic regularization is useful when sparse couplings are desired. The density of the optimal coupling is described by two functions called potentials; equivalently, potentials can be defined as a…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
We establish several quantitative stability estimates for optimal transport maps between non-degenerate densities on uniformly convex domains for the quadratic cost. Under H\"older regularity assumptions, we prove Lipschitz $L^2$…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
We present a minimization problem with a horizontal divergence-type constraint in the Heisenberg group. Our study explores its dual formulation and examines its relationship with the congested optimal transport problem, for $1 < p <…
We propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to…
We develop a theory of optimal transport relative to a distinguished subset, which acts as a reservoir of mass, allowing us to compare measures of different total variation. This relative transportation problem has an optimal solution and…