English
Related papers

Related papers: Minimum Wasserstein distance estimator under covar…

200 papers

In prescriptive analytics, the decision-maker observes historical samples of $(X, Y)$, where $Y$ is the uncertain problem parameter and $X$ is the concurrent covariate, without knowing the joint distribution. Given an additional covariate…

Optimization and Control · Mathematics 2021-06-11 Tianyu Wang , Ningyuan Chen , Chun Wang

Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optimal transport distance between L\'{e}vy measures to solve a…

Statistics Theory · Mathematics 2023-09-18 Marta Catalano , Hugo Lavenant , Antonio Lijoi , Igor Prünster

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…

Optimization and Control · Mathematics 2020-06-15 Julie Delon , Agnes Desolneux

We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…

Analysis of PDEs · Mathematics 2024-12-23 Martin Burger , Matthias Erbar , Franca Hoffmann , Daniel Matthes , André Schlichting

We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…

Optimization and Control · Mathematics 2025-12-25 Dominic S. T. Keehan , Edward J. Anderson , Wolfram Wiesemann

To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein…

Methodology · Statistics 2023-09-06 Xingyu Yan , Xinyu Zhang , Peng Zhao

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the…

Statistics Theory · Mathematics 2012-01-24 Florian Gach , Benedikt M. Pötscher

Many existing covariate shift adaptation methods estimate sample weights given to loss values to mitigate the gap between the source and the target distribution. However, estimating the optimal weights typically involves computationally…

Machine Learning · Statistics 2024-07-01 François Portier , Lionel Truquet , Ikko Yamane

We study the behavior of the Wasserstein-$2$ distance between discrete measures $\mu$ and $\nu$ in $\mathbb{R}^d$ when both measures are smoothed by small amounts of Gaussian noise. This procedure, known as Gaussian-smoothed optimal…

Statistics Theory · Mathematics 2022-06-15 Yunzi Ding , Jonathan Niles-Weed

Full-waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE-constrained optimization is used to determine unknown parameters in a wave equation that represent geophysical properties. The…

Numerical Analysis · Mathematics 2021-04-02 Bjorn Engquist , Yunan Yang

Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which…

Methodology · Statistics 2026-03-10 Junyoung Park , Irina Gaynanova

Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…

Optimization and Control · Mathematics 2026-05-28 Tam Le

We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the…

Probability · Mathematics 2021-02-26 Ivan Nourdin , Giovanni Peccati , Xiaochuan Yang

The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…

Machine Learning · Computer Science 2026-02-10 Eduardo Figueiredo , Steven Adams , Luca Laurenti

Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…

Optimization and Control · Mathematics 2026-02-09 Siyi Wang , Zifan Wang , Karl H. Johansson

We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.…

Operator Algebras · Mathematics 2015-03-13 Francesco D'Andrea , Pierre Martinetti

The adapted Wasserstein ($AW$) distance refines the classical Wasserstein ($W$) distance by incorporating the temporal structure of stochastic processes. This makes the $AW$-distance well-suited as a robust distance for many dynamic…

Probability · Mathematics 2025-10-24 Beatrice Acciaio , Songyan Hou , Gudmund Pammer

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

Statistics Theory · Mathematics 2019-11-05 Jérémie Bigot , Elsa Cazelles , Nicolas Papadakis

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Machine Learning · Statistics 2017-10-23 Nicolas Courty , Rémi Flamary , Mélanie Ducoffe

We investigate the asymptotic behavior of parametric Bayes estimators under a broad class of loss functions that extend beyond the classical translation-invariant setting. To this end, we develop a unified theoretical framework for loss…

Statistics Theory · Mathematics 2026-03-16 Robin Requadt , Housen Li , Axel Munk