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The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation…

Machine Learning · Statistics 2024-12-23 Anish Chakrabarty , Arkaprabha Basu , Swagatam Das

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any…

Machine Learning · Computer Science 2017-11-21 Yukun Chen , Jianbo Ye , Jia Li

The Gromov-Wasserstein (GW) distance has gained increasing interest in the machine learning community in recent years, as it allows for the comparison of measures in different metric spaces. To overcome the limitations imposed by the equal…

Machine Learning · Computer Science 2025-03-28 Yikun Bai , Rocio Diaz Martin , Abihith Kothapalli , Hengrong Du , Xinran Liu , Soheil Kolouri

Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide…

Machine Learning · Computer Science 2023-10-31 Lemin Kong , Jiajin Li , Jianheng Tang , Anthony Man-Cho So

The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport…

Machine Learning · Computer Science 2025-11-14 Moritz Piening , Robert Beinert

The Gromov-Wasserstein (GW) problem provides a powerful framework for aligning heterogeneous datasets by matching their internal structures in a way that minimizes distortion. However, GW alignment is sensitive to data contamination by…

Statistics Theory · Mathematics 2025-06-27 Xiaoyun Gong , Sloan Nietert , Ziv Goldfeld

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…

Optimization and Control · Mathematics 2026-04-07 Hoang Anh Tran , Binh Tuan Nguyen , Yong Sheng Soh

The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…

Analysis of PDEs · Mathematics 2024-11-25 Sangmin Park , Dejan Slepčev

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any…

Machine Learning · Computer Science 2016-08-08 Yukun Chen , Jianbo Ye , Jia Li

We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible…

Machine Learning · Computer Science 2026-05-14 Ashkan Shahbazi , Xinran Liu , Ping He , Soheil Kolouri

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high…

Machine Learning · Computer Science 2023-01-10 Mengyu Li , Jun Yu , Hongteng Xu , Cheng Meng

Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…

Machine Learning · Statistics 2023-10-31 Guillaume Mahey , Laetitia Chapel , Gilles Gasso , Clément Bonet , Nicolas Courty

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…

Machine Learning · Statistics 2020-06-18 Tam Le , Nhat Ho , Makoto Yamada

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…

Machine Learning · Statistics 2026-03-04 Khai Nguyen , Hai Nguyen , Nhat Ho

Gromov-Wasserstein (GW) distances are combinations of Gromov-Hausdorff and Wasserstein distances that allow the comparison of two different metric measure spaces (mm-spaces). Due to their invariance under measure- and distance-preserving…

Optimization and Control · Mathematics 2023-07-14 Florian Beier , Robert Beinert , Gabriele Steidl

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…

Machine Learning · Statistics 2019-05-14 Titouan Vayer , Laetitia Chapel , Rémi Flamary , Romain Tavenard , Nicolas Courty

Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific…

Machine Learning · Computer Science 2022-03-02 Cédric Vincent-Cuaz , Rémi Flamary , Marco Corneli , Titouan Vayer , Nicolas Courty

The ability to align points across two related yet incomparable point clouds (e.g. living in different spaces) plays an important role in machine learning. The Gromov-Wasserstein (GW) framework provides an increasingly popular answer to…

Machine Learning · Computer Science 2023-02-07 Meyer Scetbon , Gabriel Peyré , Marco Cuturi

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the…

Machine Learning · Computer Science 2019-02-04 Soheil Kolouri , Kimia Nadjahi , Umut Simsekli , Roland Badeau , Gustavo K. Rohde

Inspired by the Kantorovich formulation of optimal transport distance between probability measures on a metric space, Gromov-Wasserstein (GW) distances comprise a family of metrics on the space of isomorphism classes of metric measure…

Metric Geometry · Mathematics 2024-10-07 Facundo Mémoli , Tom Needham