English
Related papers

Related papers: DPOT: A DeepParticle method for Computation of Opt…

200 papers

Out-of-distribution (OOD) data poses serious challenges in deployed machine learning models as even subtle changes could incur significant performance drops. Being able to estimate a model's performance on test data is important in practice…

Machine Learning · Computer Science 2023-02-13 Yuzhe Lu , Zhenlin Wang , Runtian Zhai , Soheil Kolouri , Joseph Campbell , Katia Sycara

We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…

Numerical Analysis · Mathematics 2026-05-21 Minh-Nhat Phung , Minh-Binh Tran

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set…

Computer Vision and Pattern Recognition · Computer Science 2024-03-18 Mohammad Shifat E Rabbi , Naqib Sad Pathan , Shiying Li , Yan Zhuang , Abu Hasnat Mohammad Rubaiyat , Gustavo K Rohde

Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…

Optimization and Control · Mathematics 2023-01-18 Thibault Séjourné , Jean Feydy , François-Xavier Vialard , Alain Trouvé , Gabriel Peyré

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

Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…

Econometrics · Economics 2026-01-22 Yinchu Zhu , Ilya O. Ryzhov

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

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…

Machine Learning · Computer Science 2023-05-31 Ching-Yao Chuang , Stefanie Jegelka , David Alvarez-Melis

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation…

Analysis of PDEs · Mathematics 2018-09-20 Hugo Lavenant , Sebastian Claici , Edward Chien , Justin Solomon

Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…

Computer Vision and Pattern Recognition · Computer Science 2020-03-17 Guansong Lu , Zhiming Zhou , Jian Shen , Cheng Chen , Weinan Zhang , Yong Yu

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

We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of…

Machine Learning · Statistics 2022-02-25 Khang Le , Huy Nguyen , Tung Pham , Nhat Ho

We present a neural framework for learning conditional optimal transport (OT) maps between probability distributions. Our approach introduces a conditioning mechanism capable of processing both categorical and continuous conditioning…

Machine Learning · Computer Science 2026-04-02 Carlos Rodriguez-Pardo , Leonardo Chiani , Emanuele Borgonovo , Massimo Tavoni

Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…

Statistics Theory · Mathematics 2024-05-14 Tao Wang , Ziv Goldfeld

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

Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on…

Machine Learning · Statistics 2021-01-07 Kilian Fatras , Younes Zine , Szymon Majewski , Rémi Flamary , Rémi Gribonval , Nicolas Courty

Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…

Machine Learning · Computer Science 2022-08-08 Dandan Guo , Zhuo Li , Meixi Zheng , He Zhao , Mingyuan Zhou , Hongyuan Zha

We analyze several optimal transportation problems between de-terminantal point processes. We show how to estimate some of the distances between distributions of DPP they induce. We then apply these results to evaluate the accuracy of a new…

Data Structures and Algorithms · Computer Science 2020-11-03 Laurent Decreusefond , Guillaume Moroz

Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…

Optimization and Control · Mathematics 2019-04-10 Rui Zhang , Quanyan Zhu

Learning conditional distributions $\pi^*(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^*$. However, acquiring paired data samples is often…