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Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…

Machine Learning · Computer Science 2021-10-14 Mokhtar Z. Alaya , Gilles Gasso , Maxime Berar , Alain Rakotomamonjy

Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…

Machine Learning · Statistics 2026-03-13 Lea Kunkel

This short note is on a property of the $\mathcal{W}_2$ Wasserstein distance which indicates that independent elliptical distributions minimize their $\mathcal{W}_2$ Wasserstein distance from given independent elliptical distributions with…

Statistics Theory · Mathematics 2020-12-08 Song Fang , Quanyan Zhu

This paper proposes a unit commitment (UC) model based on data-driven Wasserstein distributionally robust optimization (WDRO) for power systems under uncertainty of renewable generation as well as its tractable exact reformulation. The…

Systems and Control · Electrical Eng. & Systems 2022-08-17 Youngchae Cho , Insoon Yang

In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…

Systems and Control · Electrical Eng. & Systems 2025-06-13 Eduardo Figueiredo , Steven Adams , Peyman Mohajerin Esfahani , Luca Laurenti

Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as…

Machine Learning · Statistics 2020-06-23 Yongchan Kwon , Wonyoung Kim , Joong-Ho Won , Myunghee Cho Paik

Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…

Machine Learning · Computer Science 2023-02-14 Hoang Phan , Trung Le , Trung Phung , Tuan Anh Bui , Nhat Ho , Dinh Phung

The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…

Machine Learning · Statistics 2023-03-02 Sloan Nietert , Rachel Cummings , Ziv Goldfeld

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…

Statistics Theory · Mathematics 2020-04-30 Jonathan Niles-Weed , Quentin Berthet

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…

Machine Learning · Computer Science 2026-05-08 Vinit Ranjan , Jisun Park , Bartolomeo Stellato

Demographic parity (DP) is a widely used group fairness criterion requiring predictive distributions to be invariant across sensitive groups. While natural in classification, full distributional DP is often overly restrictive in regression…

Machine Learning · Statistics 2026-03-27 Arthur Charpentier , Christophe Denis , Romuald Elie , Mohamed Hebiri , François HU

In the standard use case of Algorithmic Fairness, the goal is to eliminate the relationship between a sensitive variable and a corresponding score. Throughout recent years, the scientific community has developed a host of definitions and…

Machine Learning · Statistics 2024-03-28 François Hu , Philipp Ratz , Arthur Charpentier

Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized…

Machine Learning · Statistics 2025-12-16 Jie Wang

In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we…

Classical Analysis and ODEs · Mathematics 2019-11-15 Amir Sagiv

We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambiguity set centered at past observations. While this paradigm…

Machine Learning · Computer Science 2026-02-25 Guixian Chen , Salar Fattahi , Soroosh Shafiee

Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…

Machine Learning · Computer Science 2018-05-23 Maziar Sanjabi , Jimmy Ba , Meisam Razaviyayn , Jason D. Lee

The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without assuming convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many interesting…

Optimization and Control · Mathematics 2026-03-09 Immanuel M. Bomze , Daniel de Vicente , Abdel Lisser , Heng Zhang

Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…

Optimization and Control · Mathematics 2023-03-24 Waïss Azizian , Franck Iutzeler , Jérôme Malick

Policy optimization is a core component of reinforcement learning (RL), and most existing RL methods directly optimize parameters of a policy based on maximizing the expected total reward, or its surrogate. Though often achieving…

Machine Learning · Computer Science 2018-08-10 Ruiyi Zhang , Changyou Chen , Chunyuan Li , Lawrence Carin

Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…

Probability · Mathematics 2013-01-03 Larry Goldstein , Gesine Reinert