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相关论文: On Efficient Optimal Transport: An Analysis of Gre…

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Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…

机器学习 · 统计学 2018-02-21 Mathieu Blondel , Vivien Seguy , Antoine Rolet

Computing optimal transport (OT) distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. In this paper, we study the problem of approximating the general OT distance…

数据结构与算法 · 计算机科学 2023-01-18 Zhao Song , Tianyi Zhou

We consider the numerical solution of the discrete multi-marginal optimal transport (MOT) by means of the Sinkhorn algorithm. In general, the Sinkhorn algorithm suffers from the curse of dimensionality with respect to the number of…

最优化与控制 · 数学 2023-02-22 Fatima Antarou Ba , Michael Quellmalz

We propose Acc-Sinkhorn, a simple accelerated variant of Sinkhorn for entropy-regularized optimal transport (EOT). The method is derived from a bilevel optimization view: Sinkhorn row scaling solves the inner variable $u$ exactly and…

最优化与控制 · 数学 2026-05-29 Zeyi Xu , Long Chen

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…

机器学习 · 计算机科学 2024-06-21 Gen Li , Yanxi Chen , Yu Huang , Yuejie Chi , H. Vincent Poor , Yuxin Chen

Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance,…

数据结构与算法 · 计算机科学 2018-02-08 Jason Altschuler , Jonathan Weed , Philippe Rigollet

Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off,…

机器学习 · 计算机科学 2024-08-22 Lénaïc Chizat

We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…

数据结构与算法 · 计算机科学 2020-07-07 Yihe Dong , Yu Gao , Richard Peng , Ilya Razenshteyn , Saurabh Sawlani

An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…

最优化与控制 · 数学 2025-07-28 Jacob J. M. Francis , Colin J. Cotter , Marion P. Mittermaier

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…

统计理论 · 数学 2026-02-04 Tao Wang , Ziv Goldfeld

This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…

概率论 · 数学 2019-11-19 Simone Di Marino , Augusto Gerolin

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…

机器学习 · 计算机科学 2021-10-29 Khang Le , Huy Nguyen , Quang Nguyen , Tung Pham , Hung Bui , Nhat Ho

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…

机器学习 · 计算机科学 2022-04-06 Johannes Gasteiger , Marten Lienen , Stephan Günnemann

While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…

机器学习 · 统计学 2023-04-06 James Thornton , Marco Cuturi

Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better…

机器学习 · 统计学 2020-08-04 François-Pierre Paty , Marco Cuturi

Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…

机器学习 · 计算机科学 2021-07-20 Dongsheng An , Na Lei , Xianfeng Gu

We study the Unbalanced Optimal Transport (UOT) between two measures of possibly different masses with at most $n$ components, where the marginal constraints of standard Optimal Transport (OT) are relaxed via Kullback-Leibler divergence…

最优化与控制 · 数学 2024-01-09 Quang Minh Nguyen , Hoang H. Nguyen , Yi Zhou , Lam M. Nguyen

Partial Optimal Transport (POT) addresses the problem of transporting only a fraction of the total mass between two distributions, making it suitable when marginals have unequal size or contain outliers. While Sinkhorn-based methods are…

机器学习 · 计算机科学 2026-04-07 Nghia Thu Truong , Qui Phu Pham , Quang Nguyen , Dung Luong , Mai Tran

Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…

机器学习 · 计算机科学 2026-05-12 Di Wu , Ling Liang , Haizhao Yang