Related papers: Optimal Transport with Tempered Exponential Measur…
We consider ultraweak variational formulations for (parametrized) linear first order transport equations in time and/or space. Computationally feasible pairs of optimally stable trial and test spaces are presented, starting with a suitable…
Selecting input features of top relevance has become a popular method for building self-explaining models. In this work, we extend this selective rationalization approach to text matching, where the goal is to jointly select and align text…
In many statistical settings, two types of data are available: coupled data, which preserve the joint structure among variables but are limited in size due to cost or privacy constraints, and marginal data, which are available at larger…
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the…
In this paper, we study the Entropic Martingale Optimal Transport (EMOT) problem on \mathbb{R}. The investigation of the EMOT problem arises in the calibration problem of the Stochastic Volatility Models, where martingale constraints…
Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between…
We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
We design optimal trajectories to transport cold atoms in anharmonic traps, combining invariant-based inverse engineering, perturbation theory, and optimal control theory. The anharmonic perturbation energy is minimized constraining the…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix…
In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This…
We adapt the problem of continuous congested optimal transport to the Heisenberg group, equipped with a sub-Riemannian metric. Originally introduced in the Euclidean setting by Carlier, Jimenez, and Santambrogio as a path-dependent variant…
We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, $\mu$, admits a density over $\mathbb{R}^d$. For a semi-concave cost function…
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance,…
We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove…
We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr\"odinger potentials describing the density of the optimal…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…