Related papers: Private Wasserstein Distance
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…
This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…
As a fundamental problem of natural language processing, it is important to measure the distance between different documents. Among the existing methods, the Word Mover's Distance (WMD) has shown remarkable success in document semantic…
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…
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…
In this work, we study face verification in datasets where images of the same individuals exhibit significant age differences. This poses a major challenge for current face recognition and verification techniques. To address this issue, we…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
In this work we analyse a number of variants of the Wasserstein distance which allow to focus the classification on the prescribed parts (fragments) of classified 2D curves. These variants are based on the use of a number of discrete…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
Change point detection for time series analysis is a difficult and important problem in applied statistics, for which a variety of approaches have been developed in the past several decades. Here, the Wasserstein metric is employed as a…
We use Stein's method to bound the Wasserstein distance of order $2$ between a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic…
The validation of global climate models is crucial to ensure the accuracy and efficacy of model output. We introduce the spherical convolutional Wasserstein distance to more comprehensively measure differences between climate models and…
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…