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Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints. Outlier robust OT variants have been proposed based on the definition that outliers are samples which are expensive to move. In this…

Machine Learning · Statistics 2022-06-27 Kilian Fatras

Matching a source to a target probability measure is often solved by instantiating a linear optimal transport (OT) problem, parameterized by a ground cost function that quantifies discrepancy between points. When these measures live in the…

Machine Learning · Computer Science 2023-11-27 Othmane Sebbouh , Marco Cuturi , Gabriel Peyré

This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…

Optimization and Control · Mathematics 2023-09-08 Liviu Aolaritei , Nicolas Lanzetti , Hongruyu Chen , Florian Dörfler

We statistically analyze empirical plug-in estimators for unbalanced optimal transport (UOT) formalisms, focusing on the Kantorovich-Rubinstein distance, between general intensity measures based on observations from spatio-temporal point…

Statistics Theory · Mathematics 2025-09-05 Marina Struleva , Shayan Hundrieser , Dominic Schuhmacher , Axel Munk

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) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account…

Machine Learning · Computer Science 2021-10-08 Pratik Jawanpuria , N T V Satyadev , Bamdev Mishra

Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…

Machine Learning · Computer Science 2024-07-23 Athina Sotiropoulou , David Alvarez-Melis

Despite the success of contrastive learning (CL) in vision and language, its theoretical foundations and mechanisms for building representations remain poorly understood. In this work, we build connections between noise contrastive…

Machine Learning · Computer Science 2025-02-28 Zihao Chen , Chi-Heng Lin , Ran Liu , Jingyun Xiao , Eva L Dyer

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

We demonstrate the effectiveness of one of the many multi-tracer analyses enabled by Optimal Transport (OT) reconstruction. Leveraging a semi-discrete OT algorithm, we determine the displacements between initial and observed positions of…

Cosmology and Nongalactic Astrophysics · Physics 2024-03-19 Farnik Nikakhtar , Ravi K. Sheth , Nikhil Padmanabhan , Bruno Lévy , Roya Mohayaee

Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not…

Machine Learning · Computer Science 2026-05-07 Philip Naumann , Jacob Kauffmann , Klaus-Robert Müller , Grégoire Montavon

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally…

Machine Learning · Computer Science 2025-07-09 Sonia Mazelet , Rémi Flamary , Bertrand Thirion

We develop a statistical inference method for an optimal transport map between distributions on real numbers with uniform confidence bands. The concept of optimal transport (OT) is used to measure distances between distributions, and OT…

Statistics Theory · Mathematics 2024-02-16 Donlapark Ponnoprat , Ryo Okano , Masaaki Imaizumi

Systematics contaminate observables, leading to distribution shifts relative to theoretically simulated signals-posing a major challenge for using pre-trained models to label such observables. Since systematics are often poorly understood…

Instrumentation and Methods for Astrophysics · Physics 2025-11-18 Sultan Hassan , Sambatra Andrianomena , Benjamin D. Wandelt

Semantically coherent out-of-distribution (SCOOD) detection aims to discern outliers from the intended data distribution with access to unlabeled extra set. The coexistence of in-distribution and out-of-distribution samples will exacerbate…

Computer Vision and Pattern Recognition · Computer Science 2023-03-22 Fan Lu , Kai Zhu , Wei Zhai , Kecheng Zheng , Yang Cao

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

Machine Learning · Computer Science 2023-11-27 Clément Bonet

Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The…

Machine Learning · Statistics 2021-05-27 Caroline Moosmüller , Alexander Cloninger

The inherent safety alignment of Large Language Models (LLMs) is prone to erosion during fine-tuning, even when using seemingly innocuous datasets. While existing defenses attempt to mitigate this via data selection, they typically rely on…

Machine Learning · Computer Science 2026-01-13 Haozhong Wang , Zhuo Li , Yibo Yang , He Zhao , Hongyuan Zha , Dandan Guo

Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This…

Statistics Theory · Mathematics 2024-03-12 Francisco Andrade , Gabriel Peyre , Clarice Poon

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…