相关论文: Computing Kantorovich-Wasserstein Distances on $d$…

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…

Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…

We study the problem of robustly learning multi-dimensional histograms. A $d$-dimensional function $h: D \rightarrow \mathbb{R}$ is called a $k$-histogram if there exists a partition of the domain $D \subseteq \mathbb{R}^d$ into $k$…

The classical Kantorovich-Rubinstein duality theorem establishes a significant connection between Monge optimal transport and maximization of a linear form on the set of 1-Lipschitz functions. This result has been widely used in various…

In the last ten years, full-waveform inversion has emerged as a robust and efficient high-resolution velocity model-building tool for seismic imaging, with the unique ability to recover complex subsurface structures. Originally based on a…

While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on…

We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…

We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…

In this work, we propose a novel approach for subgraph matching, the problem of finding a given query graph in a large source graph, based on the fused Gromov-Wasserstein distance. We formulate the subgraph matching problem as a partial…

An upper bound for the Kantorovich transport distance between probability measures on multidimensional Euclidean spaces is given in terms of transport distances between one dimensional projections. This quantifies the Cram\'er-Wold…

Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…

We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.…

We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…

It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…

A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…

Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…

Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities…

The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…

In this paper, we propose a new method to compute the solution of time-dependent Schr\"odinger equation (TDSE). Using push-forward maps and Wasserstein Hamiltonian flow, we reformulate the TDSE as a Hamiltonian system in terms of…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…