Related papers: Tangential Fixpoint Iterations for Gromov-Wasserst…
Various statistical tasks, including sampling or computing Wasserstein barycenters, can be reformulated as fixed-point problems for operators on probability distributions. Accelerating standard fixed-point iteration schemes provides a…
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…
We study rates of convergence for estimation of the Gromov-Wasserstein (GW) distance. For two marginals supported on compact subsets of $\R^{d_x}$ and $\R^{d_y}$, respectively, with $\min \{ d_x,d_y \} > 4$, prior work established the rate…
Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures. We provide an $O(\sqrt{N/n})$…
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 introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or treelike structure with a particular direction of orientation. Our…
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we…
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…
Semantic correspondence is essential for handling diverse in-the-wild images lacking explicit correspondence annotations. While recent 2D foundation models offer powerful features, adapting them for unsupervised learning via…
We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only…
With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…
We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure…
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the Minimum Mutual Information property, namely the…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to…
We consider synthesis and analysis of probability measures using the entropy-regularized Wasserstein-2 cost and its unbiased version, the Sinkhorn divergence. The synthesis problem consists of computing the barycenter, with respect to these…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…
Computing Wasserstein barycenters of discrete measures has recently attracted considerable attention due to its wide variety of applications in data science. In general, this problem is NP-hard, calling for practical approximative…
Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal…