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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

Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of…

Computer Vision and Pattern Recognition · Computer Science 2026-01-30 Keke Tang , Ziyong Du , Xiaofei Wang , Weilong Peng , Peican Zhu , Zhihong Tian

Semi-supervised learning has made remarkable strides by effectively utilizing a limited amount of labeled data while capitalizing on the abundant information present in unlabeled data. However, current algorithms often prioritize aligning…

Computer Vision and Pattern Recognition · Computer Science 2024-05-31 Zhiquan Tan , Kaipeng Zheng , Weiran Huang

Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…

Statistics Theory · Mathematics 2022-06-08 Ziv Goldfeld , Kengo Kato , Gabriel Rioux , Ritwik Sadhu

Transformers excel in natural language processing and computer vision tasks. However, they still face challenges in generalizing to Out-of-Distribution (OOD) datasets, i.e. data whose distribution differs from that seen during training. OOD…

Machine Learning · Computer Science 2026-01-30 Yijin Zhou , Yutang Ge , Wenyuan Xie , Linqian Zeng , Xiaowen Dong , Yuguang Wang

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

We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new…

Machine Learning · Statistics 2026-05-28 M. Generali Lince , S. Gaucher , J-J. Vie , P. Loiseau

We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently…

Recent studies have shown that the performance of forgery detection can be improved with diverse and challenging Deepfakes datasets. However, due to the lack of Deepfakes datasets with large variance in appearance, which can be hardly…

Computer Vision and Pattern Recognition · Computer Science 2020-11-06 Hao Zhu , Chaoyou Fu , Qianyi Wu , Wayne Wu , Chen Qian , Ran He

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

The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order…

Computer Vision and Pattern Recognition · Computer Science 2022-04-08 Daniel Shalam , Simon Korman

Unsupervised domain adaptation (UDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain. In this paper, we introduce a novel approach called class-aware optimal transport (OT), which measures the OT…

Machine Learning · Computer Science 2024-01-30 Tuan Nguyen , Van Nguyen , Trung Le , He Zhao , Quan Hung Tran , Dinh Phung

Ensuring fairness has emerged as one of the primary concerns in AI and its related algorithms. Over time, the field of machine learning fairness has evolved to address these issues. This paper provides an extensive overview of this field…

Machine Learning · Computer Science 2024-11-15 Quan Zhou

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…

Machine Learning · Computer Science 2022-03-08 Litu Rout , Alexander Korotin , Evgeny Burnaev

Detecting out-of-distribution (OOD) samples plays a key role in open-world and safety-critical applications such as autonomous systems and healthcare. Recently, self-supervised representation learning techniques (via contrastive learning…

Computer Vision and Pattern Recognition · Computer Science 2021-10-12 Sina Mohseni , Arash Vahdat , Jay Yadawa

Machine learning based systems are reaching society at large and in many aspects of everyday life. This phenomenon has been accompanied by concerns about the ethical issues that may arise from the adoption of these technologies. ML fairness…

Machine Learning · Computer Science 2021-01-01 Luca Oneto , Silvia Chiappa

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

To fix the 'bias in, bias out' problem in fair machine learning, it is important to steer feature distributions of data or internal representations of Large Language Models (LLMs) to ideal ones that guarantee group-fair outcomes. Previous…

Machine Learning · Computer Science 2025-10-27 Mohit Sharma , Amit Jayant Deshpande , Chiranjib Bhattacharyya , Rajiv Ratn Shah

The goal of optimal transport (OT) is to find optimal assignments or matchings between data sets which minimize the total cost for a given cost function. However, sometimes the cost function is unknown but we have access to (parts of) the…

Optimization and Control · Mathematics 2026-05-28 Alberto González-Sanz , Michel Groppe , Axel Munk

Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…

Machine Learning · Computer Science 2023-08-08 Yikun Bai , Berhnard Schmitzer , Mathew Thorpe , Soheil Kolouri
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