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We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…

Machine Learning · Statistics 2024-04-01 Jie Wang , Rui Gao , Yao Xie

We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the…

Statistics Theory · Mathematics 2025-02-25 Victor-Emmanuel Brunel , Jordan Serres

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $F$ and $G$ on $\mathbb R$. The estimator is based on the order statistics of (possibly dependent)…

Statistics Theory · Mathematics 2017-10-31 Philippe Berthet , Jean-Claude Fort , Thierry Klein

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the…

Optimization and Control · Mathematics 2018-03-13 Bernhard Schmitzer , Benedikt Wirth

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

Machine Learning · Computer Science 2018-11-16 Alain Rakotomamonjy , Abraham Traoré , Maxime Berar , Rémi Flamary , Nicolas Courty

We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and…

Data Analysis, Statistics and Probability · Physics 2019-04-10 Ilya Mandel , Will M. Farr , Jonathan R. Gair

Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular…

Optimization and Control · Mathematics 2026-05-13 Peng Xu , Changbo Zhu , Xiaohui Chen

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

Methodology · Statistics 2022-02-14 Ryo Okano , Masaaki Imaizumi

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…

Statistics Theory · Mathematics 2025-04-25 Keunwoo Lim , Ting Ye , Fang Han

Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…

Statistics Theory · Mathematics 2021-01-01 Shun-ichi Amari , Takeru Matsuda

We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…

Machine Learning · Statistics 2025-05-29 Gabriele Visentin , Patrick Cheridito

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…

Statistics Theory · Mathematics 2019-07-09 Ankit Pensia , Varun Jog , Po-Ling Loh

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

Methodology · Statistics 2026-01-08 Yuanying Chen , Tongyu Li , Yang Bai , Zhenhua Lin

The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…

Metric Geometry · Mathematics 2024-10-01 Roan Talbut , Daniele Tramontano , Yueqi Cao , Mathias Drton , Anthea Monod

The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong…

Statistics Theory · Mathematics 2024-10-14 Stanislav Minsker , Shunan Yao

Fairness testing evaluates whether a model satisfies a specified fairness criterion across different groups, yet most research has focused on classification models, leaving regression models underexplored. This paper introduces a framework…

Machine Learning · Computer Science 2026-02-11 Wanxin Li , Yongjin P. Park , Khanh Dao Duc

We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…

Atmospheric and Oceanic Physics · Physics 2020-11-16 Gabriele Vissio , Valerio Lembo , Valerio Lucarini , Michael Ghil

We define a metric in the space of positive finite positive measures that extends the 2-Wasserstein metric, i.e. its restriction to the set of probability measures is the 2-Wasserstein metric. We prove a dual and a dynamic formulation and…

Metric Geometry · Mathematics 2023-03-07 Hugo Leblanc , Thibaut Le Gouic , Jacques Liandrat , Magali Tournus

The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will…

Methodology · Statistics 2020-10-26 Fatemeh Ghaderinezhad , Christophe Ley , Ben Serrien

We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms.…

Methodology · Statistics 2018-12-31 Isabella Verdinelli , Larry Wasserman