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Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a…

Optimization and Control · Mathematics 2020-07-03 Arthur Mensch , Gabriel Peyré

Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…

Machine Learning · Statistics 2020-11-09 Ievgen Redko , Titouan Vayer , Rémi Flamary , Nicolas Courty

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) 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

Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…

Machine Learning · Computer Science 2024-01-23 Liangliang Shi , Zhaoqi Shen , Junchi Yan

In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…

Machine Learning · Statistics 2019-11-05 John Lee , Max Dabagia , Eva L. Dyer , Christopher J. Rozell

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…

Machine Learning · Statistics 2023-01-18 Thibault Séjourné , Gabriel Peyré , François-Xavier Vialard

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Machine Learning · Statistics 2025-07-01 Yingyuan Li , Aokun Wang , Zhongjian Wang

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) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…

Statistics Theory · Mathematics 2023-01-05 Shayan Hundrieser , Gilles Mordant , Christoph Alexander Weitkamp , Axel Munk

Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…

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) measures distances between distributions in a way that depends on the geometry of the sample space. In light of recent advances in computational OT, OT distances are widely used as loss functions in machine learning.…

Methodology · Statistics 2021-06-22 Debarghya Mukherjee , Aritra Guha , Justin Solomon , Yuekai Sun , Mikhail Yurochkin

In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…

Machine Learning · Computer Science 2025-01-30 Jianming Huang , Xun Su , Zhongxi Fang , Hiroyuki Kasai

Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…

Machine Learning · Computer Science 2021-11-15 Weijie Liu , Chao Zhang , Nenggan Zheng , Hui Qian

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

Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the…

Machine Learning · Statistics 2022-06-08 Khai Nguyen , Dang Nguyen , The-Anh Vu-Le , Tung Pham , Nhat Ho

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…

We research relations between optimal transport theory (OTT) and approximate Bayesian computation (ABC) possibly connected to relevant metrics defined on probability measures. Those of ABC are computational methods based on Bayesian…

Statistics Theory · Mathematics 2021-05-06 Marco Tarsia , Antonietta Mira , Daniele Cassani

Optimal transport (OT) is a framework that can be used to guide the optimal allocation of a limited amount of resources. The classical OT paradigm does not consider malicious attacks in its formulation and thus the designed transport plan…

Systems and Control · Electrical Eng. & Systems 2021-06-15 Jason Hughes , Juntao Chen