相关论文: Gromov-Wasserstein Distances: Entropic Regularizat…

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…

This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…

The Optimal Transport (OT) problem with squared Euclidean cost consists in finding a coupling between two input measures that maximizes correlation. Consequently, the optimal coupling is often singular with respect to the Lebesgue measure.…

We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output…

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…

The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical properties of the generated distributions, we provide a…

We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…

We investigate optimal transport (OT) for measures on graph metric spaces with different total masses. To mitigate the limitations of traditional $L^p$ geometry, Orlicz-Wasserstein (OW) and generalized Sobolev transport (GST) employ Orlicz…

The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…

We statistically analyze empirical plug-in estimators for unbalanced optimal transport (UOT) formalisms, focusing on the Kantorovich-Rubinstein distance, between general intensity measures based on observations from spatio-temporal point…

Generative Adversarial Networks are a popular method for learning distributions from data by modeling the target distribution as a function of a known distribution. The function, often referred to as the generator, is optimized to minimize…

Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…

We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is…

Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…

\emph{Optimal Transport} (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of…

We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous…

Gromov-Wasserstein (GW) transport is inherently invariant under isometric transformations of the data. Having this property in mind, we propose to estimate dynamical systems by transfer operators derived from GW transport plans, when merely…

Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…

We study optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying…

Comparing two probability measures supported on heterogeneous spaces is an increasingly important problem in machine learning. Such problems arise when comparing for instance two populations of biological cells, each described with its own…