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We analyze two algorithms for approximating the general optimal transport (OT) distance between two discrete distributions of size $n$, up to accuracy $\varepsilon$. For the first algorithm, which is based on the celebrated Sinkhorn's…

Data Structures and Algorithms · Computer Science 2018-06-08 Pavel Dvurechensky , Alexander Gasnikov , Alexey Kroshnin

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…

Data Structures and Algorithms · Computer Science 2023-01-18 Zhao Song , Tianyi Zhou

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 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

Given a $d$-dimensional continuous (resp. discrete) probability distribution $\mu$ and a discrete distribution $\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass…

Computational Geometry · Computer Science 2023-11-07 Pankaj K. Agarwal , Sharath Raghvendra , Pouyan Shirzadian , Keegan Yao

When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…

Machine Learning · Computer Science 2024-01-23 Chuanwen Feng , Wenlong Chen , Ao Ke , Yilong Ren , Xike Xie , S. Kevin Zhou

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…

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

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…

Machine Learning · Computer Science 2024-06-21 Gen Li , Yanxi Chen , Yu Huang , Yuejie Chi , H. Vincent Poor , Yuxin Chen

Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…

Machine Learning · Computer Science 2022-03-09 Nathaniel Lahn , Sharath Raghvendra , Kaiyi Zhang

Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…

Machine Learning · Statistics 2014-03-25 Marco Cuturi

Optimal transport (OT) has become a widely used tool in the machine learning field to measure the discrepancy between probability distributions. For instance, OT is a popular loss function that quantifies the discrepancy between an…

Machine Learning · Computer Science 2022-12-27 Shintaro Nakamura , Han Bao , Masashi Sugiyama

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…

Machine Learning · Statistics 2023-04-17 Tianlin Liu , Joan Puigcerver , Mathieu Blondel

In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…

Machine Learning · Statistics 2022-01-12 Nicolas Keriven

Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To…

Machine Learning · Statistics 2026-04-07 Mengyu Li , Jun Yu , Tao Li , Cheng Meng

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…

Data Structures and Algorithms · Computer Science 2020-07-07 Yihe Dong , Yu Gao , Richard Peng , Ilya Razenshteyn , Saurabh Sawlani

This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…

Optimization and Control · Mathematics 2023-01-25 Yiling Luo , Yiling Xie , Xiaoming Huo

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…

Machine Learning · Statistics 2017-10-23 Aude Genevay , Gabriel Peyré , 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

Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…

Machine Learning · Statistics 2018-03-06 Brahim Khalil Abid , Robert M. Gower