Related papers: Domain decomposition for entropy regularized optim…
In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying…
A generalized unbalanced optimal transport distance ${\rm WB}_{\Lambda}$ on matrix-valued measures $\mathcal{M}(\Omega,\mathbb{S}_+^n)$ was defined in [arXiv:2011.05845] \`{a} la Benamou-Brenier, which extends the Kantorovich-Bures and the…
Sinkhorn divergence is a measure of dissimilarity between two probability measures. It is obtained through adding an entropic regularization term to Kantorovich's optimal transport problem and can hence be viewed as an entropically…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
The least gradient problem (minimizing the total variation with given boundary data) is equivalent, in the plane, to the Beckmann minimal-flow problem with source and target measures located on the boundary of the domain, which is in turn…
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…
Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is…
Generalizing knowledge to unseen domains, where data and labels are unavailable, is crucial for machine learning models. We tackle the domain generalization problem to learn from multiple source domains and generalize to a target domain…
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measured in Wasserstein distance, which are applicable to a wide…
In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
Cross-domain alignment between image objects and text sequences is key to many visual-language tasks, and it poses a fundamental challenge to both computer vision and natural language processing. This paper investigates a novel approach for…
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…
We show that the derivatives of the Sinkhorn-Knopp algorithm, or iterative proportional fitting procedure, converge towards the derivatives of the entropic regularization of the optimal transport problem with a locally uniform linear…