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We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…

Machine Learning · Statistics 2022-04-21 Lang Liu , Soumik Pal , Zaid Harchaoui

The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting while preserving desirable properties of the resulting goodness-of-fit (GoF) statistics. In particular, the rank energy (RE) and…

Machine Learning · Statistics 2022-11-29 Shoaib Bin Masud , Matthew Werenski , James M. Murphy , Shuchin Aeron

Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…

Numerical Analysis · Mathematics 2020-08-11 Martin Eigel , Robert Gruhlke , Manuel Marschall

In this paper, we reveal the relationship between entropy rate and the congestion in complex network and solve it analytically for special cases. Finding maximizing entropy rate will lead to an improvement of traffic efficiency, we propose…

Physics and Society · Physics 2017-09-15 Yuhang Fan , Hanyuan Liu , Shibo He

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical…

Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…

Optimization and Control · Mathematics 2025-04-10 Keiichi Morikuni , Koya Sakakibara , Asuka Takatsu

This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…

Machine Learning · Statistics 2025-01-24 Titouan Vayer , Etienne Lasalle

We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb R^d$, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption…

Statistics Theory · Mathematics 2023-05-26 Aram-Alexandre Pooladian , Vincent Divol , Jonathan Niles-Weed

Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…

Computer Vision and Pattern Recognition · Computer Science 2024-07-08 Mackenzie J. Meni , Ryan T. White , Michael Mayo , Kevin Pilkiewicz

Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper,…

Statistics Theory · Mathematics 2019-06-10 T. Tony Cai , Hongji Wei

This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…

Optimization and Control · Mathematics 2024-08-27 Yukuan Hu , Mengyu Li , Xin Liu , Cheng Meng

In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…

Optimization and Control · Mathematics 2025-07-17 Vishwak Srinivasan , Qijia Jiang

This paper presents a light-weight, high-quality texture synthesis algorithm that easily generalizes to other applications such as style transfer and texture mixing. We represent texture features through the deep neural activation vectors…

Graphics · Computer Science 2020-10-29 Eric Risser

Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…

Machine Learning · Statistics 2024-01-24 T. Tony Cai , Hongming Pu

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…

Methodology · Statistics 2017-01-02 Arnaud Dupuy , Alfred Galichon , Yifei Sun

Entropic optimal transport -- the optimal transport problem regularized by KL diver\-gence -- is highly successful in statistical applications. Thanks to the smoothness of the entropic coupling, its sample complexity avoids the curse of…

Statistics Theory · Mathematics 2025-05-09 Alberto González-Sanz , Stephan Eckstein , Marcel Nutz

This paper studies the convergence rates of optimal transport (OT) map estimators, a topic of growing interest in statistics, machine learning, and various scientific fields. Despite recent advancements, existing results rely on regularity…

Statistics Theory · Mathematics 2024-12-12 Yizhe Ding , Runze Li , Lingzhou Xue

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Machine Learning · Statistics 2025-07-01 Yingyuan Li , Aokun Wang , Zhongjian Wang

Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…

Machine Learning · Statistics 2022-06-03 Jingyi Zhang , Cheng Meng , Jun Yu , Mengrui Zhang , Wenxuan Zhong , Ping Ma

One critical component in lossy deep image compression is the entropy model, which predicts the probability distribution of the quantized latent representation in the encoding and decoding modules. Previous works build entropy models upon…

Image and Video Processing · Electrical Eng. & Systems 2023-03-16 Yichen Qian , Ming Lin , Xiuyu Sun , Zhiyu Tan , Rong Jin