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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

Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…

Data Structures and Algorithms · Computer Science 2025-01-14 Sina Moradi

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 machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…

Graphics · Computer Science 2024-02-28 Baptiste Genest , Nicolas Courty , David Coeurjolly

Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…

Machine Learning · Statistics 2025-10-15 Khai Nguyen

Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…

Machine Learning · Computer Science 2023-08-14 Oliver Struckmeier , Ievgen Redko , Anton Mallasto , Karol Arndt , Markus Heinonen , Ville Kyrki

Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…

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 resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitioners have access to samples which approximate the continuous…

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…

Machine Learning · Computer Science 2020-11-11 J. Saketha Nath , Pratik Jawanpuria

Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in…

Machine Learning · Computer Science 2023-03-15 Yasutoshi Ida , Sekitoshi Kanai , Kazuki Adachi , Atsutoshi Kumagai , Yasuhiro Fujiwara

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

Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…

Optimization and Control · Mathematics 2025-12-29 Thai P. D. Nguyen , Hong T. M. Chu , Kim-Chuan Toh

Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…

Optimization and Control · Mathematics 2024-03-11 Xun Tang , Holakou Rahmanian , Michael Shavlovsky , Kiran Koshy Thekumparampil , Tesi Xiao , Lexing Ying

The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…

Machine Learning · Statistics 2025-12-11 Sloan Nietert , Ziv Goldfeld

Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…

Machine Learning · Computer Science 2021-10-11 Bamdev Mishra , N T V Satyadev , Hiroyuki Kasai , Pratik Jawanpuria

Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…

Machine Learning · Computer Science 2024-03-08 Jaemoo Choi , Jaewoong Choi , Myungjoo Kang

We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…

Machine Learning · Computer Science 2023-11-23 Shoichiro Takeda , Yasunori Akagi , Naoki Marumo , Kenta Niwa

Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…

Machine Learning · Computer Science 2025-05-20 Peter Chen , Yue Xie , Qingpeng Zhang

Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…

Machine Learning · Statistics 2025-05-13 Gabriel Peyré