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Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…

Machine Learning · Computer Science 2026-03-05 Henri Schmidt , Peter Halmos , Ben Raphael

Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has…

Machine Learning · Statistics 2020-06-17 Yasunori Akagi , Yusuke Tanaka , Tomoharu Iwata , Takeshi Kurashima , Hiroyuki Toda

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

Numerical Analysis · Mathematics 2015-09-15 Adam M. Oberman , Yuanlong Ruan

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…

Machine Learning · Statistics 2020-11-10 Titouan Vayer

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…

Machine Learning · Computer Science 2019-06-26 Yujia Xie , Minshuo Chen , Haoming Jiang , Tuo Zhao , Hongyuan Zha

Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build…

Machine Learning · Statistics 2021-12-03 Quang Huy Tran , Hicham Janati , Ievgen Redko , Rémi Flamary , Nicolas Courty

The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…

Optimization and Control · Mathematics 2022-10-25 Nazarii Tupitsa , Pavel Dvurechensky , Darina Dvinskikh , Alexander Gasnikov

The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…

Machine Learning · Statistics 2022-09-16 Meyer Scetbon , Marco Cuturi

In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important…

Machine Learning · Computer Science 2021-04-06 Karthik S. Gurumoorthy , Pratik Jawanpuria , Bamdev Mishra

The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…

General Topology · Mathematics 2025-07-03 Yuping Lv , Qi Zhao , Xuebin Chang , Wei Zeng

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.…

Optimization and Control · Mathematics 2021-02-17 Junqi Wang , Pei Wang , Patrick Shafto

Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…

Machine Learning · Computer Science 2025-09-26 Annabel Ma , Kaiying Hou , David Alvarez-Melis , Melanie Weber

The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…

Computer Vision and Pattern Recognition · Computer Science 2025-11-04 Yan Bin Ng , Xianfeng Gu

Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account…

Machine Learning · Computer Science 2021-10-08 Pratik Jawanpuria , N T V Satyadev , Bamdev Mishra

Recently, the statistical properties of empirical Entropic Optimal Transport (EOT) have attracted great interest, as this quantity has been shown to be useful for complex data analysis, among other reasons due to its computational…

Statistics Theory · Mathematics 2026-04-15 Santiago Arenas-Velilla , Axel Munk , Luis-Alberto Rodríguez

Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…

Machine Learning · Computer Science 2025-02-04 Clément Bonet , Kimia Nadjahi , Thibault Séjourné , Kilian Fatras , Nicolas Courty

Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…

Machine Learning · Computer Science 2024-08-22 Eduardo Fernandes Montesuma , Fred Ngolè Mboula , Antoine Souloumiac

Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…

Probability · Mathematics 2023-04-26 Stephan Eckstein , Gudmund Pammer

This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each…

Optimization and Control · Mathematics 2024-09-23 Ivan Lau , Shiqian Ma , César A. Uribe

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…