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

The Gromov-Wasserstein (GW) distance serves as a powerful tool for matching objects in metric spaces. However, its traditional formulation is constrained to pairwise matching between single objects, limiting its utility in scenarios and…

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…

Although optimal transport (OT) problems admit closed form solutions in a very few notable cases, e.g. in 1D or between Gaussians, these closed forms have proved extremely fecund for practitioners to define tools inspired from the OT…

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from machine translation to transfer learning. Recently, purely unsupervised methods operating on monolingual embeddings have become effective alignment tools.…

We propose a new approach for unsupervised alignment of heterogeneous datasets, which maps data from two different domains without any known correspondences to a common metric space. Our method is based on an unbalanced optimal transport…

The Gromov-Wasserstein (GW) problem is a variant of the classical optimal transport problem that allows one to compute meaningful transportation plans between incomparable spaces. At an intuitive level, it seeks plans that minimize the…

Structured data, such as graphs, is vital in machine learning due to its capacity to capture complex relationships and interactions. In recent years, the Fused Gromov-Wasserstein (FGW) distance has attracted growing interest because it…

Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…

We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…

The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization. This paper provides convergence guarantees for…

It is well known that optimal transport suffers from the curse of dimensionality: when the prescribed marginals are approximated by i.i.d. samples, the convergence of the empirical optimal transport problem to the population counterpart…

Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…

The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing…

Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…

The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…

Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly…

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…

This paper presents a framework for computing the Gromov-Wasserstein problem between two sets of points in low dimensional spaces, where the discrepancy is the squared Euclidean norm. The Gromov-Wasserstein problem is a generalization of…

The Gromov-Wasserstein (GW) transport problem is a relaxation of classic optimal transport, which seeks a transport between two measures while preserving their internal geometry. Due to meeting this theoretical underpinning, it is a…

The empirical optimal transport (OT) cost between two probability measures from random data is a fundamental quantity in transport based data analysis. In this work, we derive novel guarantees for its convergence rate when the involved…